References 2001-2003
参考文献 [2001-2003]
これまでに印刷した論文または参考文献の一覧を作成する。
A1-A25,B1-B5は紙フォルダの名前である。
A1
- Z.Djabri, N.P.Smart, "A comparison of direct and indirect methods for computing Selmer groups of an elliptic curve", p1-12.
- R.J.Stroeker, N.Tzanakis, "Computing all integer solutions of a general elliptic equation", p1-9.
- ???, "Diophantine equations: Progress and problems", p1-33.
- Masanobu Kaneko, Katsuichi Tachibana, "When is a ploygonal pyramid number again polygonal?", Rocky Mountain Journal of Mathematics, Vol.32, No.1, 2002.
- Masanari Kida, "Good reduction of elliptic curves over imaginary quadratic fields", Journal de Th\'eorie de Nombres de Bordeau 13(2001), p201-209.
- Edward F.Earky, "Quartic ploynomials with three relative extrema and two points if inflection at integer lattice points", Nov. 21, 1995, p1-7.
- Benjamin M.M. de Weger, "S-inetgral solutions ti a Weierstrass equation", Journal de Th\'eorie de Nombres de Bordeau 9(1997), p2810391.
- N.Tzanakis, "Effective solution of two simultaneous Pell equations by Elliptic Logarithm Method", p1-20.
- Benjamin M.M. de Weger, "One diophantine equation", Dec. 1, 1995, p1-8.
- Kenji Koyama, Yukio Tsuruoka, Hiroshi Sekigawa, "On searching for solution of the Diophantine equation x^3+y^3+z^3=n", Math. of Computation, Vol. 66, No.218, 1997, p841-851.
- D.R.Heath-Brown, W.M.Lioen, H.J.J. te Riele, "On solving the Diophantine equation x^3+y^3+z^3=n on a vector computer", 1991, p1-10.
- R.J.Stroeker, N.Tzanakis, "Solving elliptic Diophantine equations by estimating leanear forms in elliptic logarithms", p1-21.
- R.J.Stroeker, Benjamin M.M. de Weger, "Solving elliptic Diophantine equations: The general cubic case", 1991, p1-28.
- J.R.Merriman, S.Siksek, N.P.Smart, "Explicit 4-descents on an elliptic curve", Acta Arithmetica LXXVII.4, 1996, p385-404.
- Michael Waldschimidt, "Elliptic curves and complex multiplication", Nov.17, 2001, p1-10.
- Nils Bruin, E.Victor Flynn, "Towers of 2-covers of hyperelliptic curves", July 9, 2001, p1-17.
- Mathhew Baker, Juji Hasegawa, "Automorphisms of $X_0^*(p)$", 1991, p1-13.
- Jan H.Bruinier, Ken Ono, "The arithmetic of Borchard's exponents", p1-11.
- Douglas Ulmer, "Explicit calculations with elliptic curves over function fields", Feb. 13, 2001, p1-4.
- Qiu Derong, Zhang Xianke, "Mordell-Weil group and Selmer groups of tow types of elliptic curves", 1991, p1-5.
- Sang Yook An, Seog Young Kim, David C. Marshall, Susan H.Marshall, William G.MaCallum, Alexabdar R.Pelis, "Jacobians of genus one curves", p1-13.
- Alexei N.Skorobogatov, "Beyond the Manin obstruction", p1-15.
- Thomas Anthony Fisher, "On 5 and 7 descents for elliptic curves", Aug. 2000, p1-128.
- Susanne Schmitt, Universita\"t des Saarlandes, "A conditional algoarithm for the computation of the rank of elliptic curves over quardatic number fields", Oct. 25, 2000, p1-20.
- Allan J.MacLeod, "A note on the curve Y^2=(X+p)(X^2+p^2)", p1-5.
- Massimo Bertolini, Henri Darmon, "p-adic priods, p-adic L-functions and the p-adic uniformization of Shimura curves", p1-31.
A2
- Steven D.Galbraith, "Rational points on $X_0^+(p)A$", Experimental Math.Vol.8(1999), No.4, 1999, p311-318.
- J.Hsu, S.Miller, "Rank of elliptic curves and the Birch Swinnerton-Dyer conjecture", p1-13.
- Heidi Lie Williams, "A Friendly introduction to elliptic curves", Nov.7, 2002, p1-10.
- Al Cuoco, "Meta-problems in mathematics", p1-7.
- Bas Edixhoven, "BSD Summer School, Paris, July 4 and 5, 2002", July 21, 2002, p1-17.
- Christophe Cornut, "Mazur's conjecture on higher Heegner points", Oct. 24, 2001, p1-28.
- J.S.Milne, "Elliptic curves", Aug. 21, 1996(v1.01), p1-158.
- J.S.Milne, "Algebraic geometry", June 13, 1998(v3.01), p1-157.
- Shouwu Zhang, "Height of Heegner points on Shimura curves", Nov. 3, 1999, p1-125.
A3
- Yuri F. Bilu, "Diophantine analysis and additive theory", p1-12.
- Michael A.Bennett, Chris M.Skinner, "Ternary Diophantine equations via Galois representations and modular forms", Aug. 8, 2002, p1-34.
- F.Brukers, C.J.Smyth, "Cyclotomic points on curves", p1-16.
- Michael A.Bennett, Vinayak Vatsal, Soroosh Yazdani, "Ternary Diophantine equations of signature (p,p,3)", p1-18.
- SZ.Tengely, "On the Diophantine equation F(x)=G(y)", 2000, p1-17.
- Johnny Edwards, "A complete solution of X^2+Y^3+Z^5=0", Nov. 29, 2001, p1-31.
- Nils Bruin, "On power sums of two cubes", March 24, 2000, p1-17.
- J.Maurice Rojas, "Uncomputability large integral points on algebraic plane curves?", Nov. 20, 1998, p1-17.
- A.Bremner, R.J.Stroeker, N.Tzanakis, "On sums of consecutive squares", 1991, p1-31.
- Istv\'an Ga\'al, G\'abor Nyul, "Computing all monogenous mixed dihedral quartic extensions of a quadratic field", Journal de Th\'eorie de Nombres de Bordeau 13(2001), p137-142.
- Guillaume Hanrot, "Solving Diophantine equations", Dec. 1, 1997, p87-90.
- Michael A.Bennett, Bruce Reznick, "Positive rational solutions to x^y=y^{mx}: a number-theoretic excursion", July 31, 2002, p1-11.
- M.Waldschmidt, "Open Diophantine Problems", March 18, 2001, p1-51.
- Jean-Marc Couveignes, Thierry Henocq, "Action of modular correspondences around CM points", March 20, 2002, p1-11.
- Avner Ash, Robert Gross, "Generalized non-Abelian reciprocity laws: A context for Wiles's proof", April 7, 2000, p1-13.
- Gerhard Frey, "Links between stable elliptic curves and certain Diophantine equations", Annales Universitiatis Saraviensus Seris Math. Vol.1, No.1, 1986, p1-40.
- B.G.Sloss, "On a Diophantine equation with four variables", April, 1997, p1-10.
- Michel Waldsschmidt, "Open Diophantine Problems", April 6, 2001, p1-26.
- Fran\c cois Hennecart, "Sum of cubes: Algorithmic and numerical aspects", Jan. 13, 1997, p1-8.
- G.Donald Allen, "Diophantine, ca.240", 2000, p1-13.
- Scott T.Parsell, "Iterative methods for pairs of additive Diophantine equations", 1991, p1-11.
- Scott T.Parsell, "Description of Search", p1-10.
- Myung-Hwan Kim, "Unsolved problems in number theory", p1-12.
- David M.Bressoud, "Computer-Generated proofs of mathematical theorems", p1-14.
- Andrej Dujella, "Diophantine quarduples for squares of Fibonacci and Lucas numbers", Portugaliae Mathemacia Vol.52 Fasc.3, 1995, p305-318.
- Harvey Dubner, "Carmichael number of the form (6m+1)(12m+1)(18m+1)", Journal of Ineteger Sequences, Vol.5, 2002, p1-8.
- Harvey Dubner, "Primes of the form (b^n+1)/(b+1)", Journal of Ineteger Sequences, Vol.3, 2002, p1-8.
- Kwang-Wu Chen, "Algorithms for Bernoulli numbers and Euler numbers", Journal of Ineteger Sequences, Vol.4, 2002, p1-7.
A4
- ???, "Six lectures on Fermat's last theorem", p1-13.
- Roland Que\^me, "A calssical approach on Fermat-Wiles Theorem Version 5.2", Jan. 20, 2002, p1-218.
- Catherine O'neil, "Explicit descent over X(3) and X(5)", p1-13.
- Qiu Derong, Zhang Xianke, "L-series and their 2-adic and 3-adic valuations at s=1 attached to CM elliptic curves", 2000, p1-30.
- Franz Lemmermeyer, "Families of non-congruent numbers", p1-17.
- Doulas Ulmer, "Elliptic curves with large rank over function fields", Sep. 19, 2001, p1-17.
A5
- Michal Mnuk, "Algebraic and geometric approach to parametrization of raional curves", Dec. 1995, PhD thesis, p1-132.
- J.E.Cremona, B.Mazur, "Visualizing elements in the Shafarevich-Tate grpoup", p1-20.
- 長尾 孝一, "rankの高い楕円曲線の構成方法について", p1-17.
- 坂田 裕, "半整数ウエイトの保型形式のフーリエ係数と保型L関数の特殊値の間に関する概説 -W.Kohnen-D.Zagierの与えた結果の紹介-", Dec. p1-33.
- 松野 一夫, "代数体の拡大でrankが増える楕円曲線について", p1-6.
- 尾崎 学, "与えられた構造の有限岩澤加群を持つZ_p-拡大の構成とその応用", p1-8.
- Massimo Bertolini, Henri Darmon, "Non-triviality of falmilies of Heegner points and rank of Selmer group over anticyclotomic towers", p1-6.
- K.Rubin, A.Silververg, "Rank frequencies for quadratic twists of elliptic curves", p1-14.
- 木田 祐司, "数体ふるい法による素因数分解", 1.4版, 1999, p1-22.
- 木田 祐司, "General Number Field Sieveについて", p1-17.
- 木田 祐司, "Number Field Sieveについて", p1-15.
A6
- D.R.Stinson, "The group operation for elliptic curves", p1-3.
- Ezra Brown, "Three Fermat trails to elliptic curves", p1-17.
- Allan J.MacLeod, "A simple practical heigher descent for large height rational points on certain elliptic curves", July 15, 2002, p1-14.
- Nikolaj M.Glazunov, "On validated numeric of values of some Zata and L-functions, and applications", p1-10.
- Amod Agashe, William Stein, "Visible evidence for the Birch and Swinnerton-Dyer conjecture for modular Abelian varaeties of rank zero", Feb. 4, 2002, p1-22.
- Janathan Hsu, "Analytic rank of elliptic curves and the Birch and Swinnerton-Dyer conjecture", Fall 2001, p1-18.
- Jerzy Browkin, "The abc-conjecture", p1-28.
A7
- Jan-Hendrik Evertse, "Diophantine equations and Diophantine approximation", p1-12.
- Michael Stoll, Tonghai Yang, "On the L-function of the curves y^2=x^5+A", Oct. 22, 2002, p1-17.
- Aaron Tievsky, "The decomposition of integers as the sums of squares in general number fields", Aug. 5, 1998, p1-14.
- ???, "Number Fields", p1-14.
- ???, "A little bit of number theory", p1-5.
- Masayuki Itakura, "Ideal theoretic approach for number theory", p1-15.
- 小川 裕之, "楕円曲線の有理点,等分点,同種写像...過去から現在へ -何が知られているか-", July. 7, 1999, p1-29.
- Koh-ichi Nagao, "An example of elliptic curve over Q with rank >= 20", p1-3.
- Koh-ichi Nagao, "An example of elliptic curve over Q with rank >= 21", p1-2.
- Koh-ichi Nagao, "An example of elliptic curve over Q(T) with rank >= 13", p1-2.
- Koh-ichi Nagao, "Q(T)-rank of elliptic curves and certain limit coming from the local points", Dec. 15, 1995, p1-20.
- Koh-ichi Nagao, "Construction pf high-rank elliptic curves with a non trivial torsion points", 1991, p1-5.
- Koh-ichi Nagao, "On the rank of elliptic curves y^2=x^3-kx", p1-5.
- Takaaki Kagawa, "実二次体上の楕円曲線の整数点の計算, および自明な導手を持つ楕円曲線の決定", 1999, p1-11.
- Takaaki Kagawa, "実二次体上至る所good reductionを持つ楕円曲線", 1999, p1-20.
- Karl Rubin, "Euler systems and modular elliptic curves", p1-15.
- Shou-Wu Zhang, "Heigth on modular curves", Oct. 21, 2000, p1-20.
- Takeshi Goto, "A study of the Selmer group of elliptic curves with a rational 2-torsion", thesis, 2000, p1-54.
- Paul M.Jenkins, "Odd perfect numbers have a prime factor exceeding 10^7", Sep., 2000, p1-50.
- Robert Pollack, Karl Rubin, "The main conjecture for CM elliptic curves at supersingular primes", 2000, p1-15.
- Barry Mazur, Karl Rubin, "Studying the growth of Mordell-Weil", 2000, p1-23.
- Barry Mazur, Karl Rubin, "Kolyvagin systems (Version 7/26/2002)", 2002, p1-82.
- Manindra Agrawal, Neeraj Kayal, Nitin Saxena, "PRIMES is in P", Aug. 6, 2002, p1-9.
A8
- Z.Djabri, Edwards Schaefer, Nigel Smart, "Computing the p-selmer group of an elliptic curve", May 26, 1999, p1-15.
- Hizuru Yamagishi, "On elliptic curves of rank four with three-division rational point", Pacific Journal of Math. Vol.206, No.1, 2002, p231-244.
- Ryotaro Okazaki, "Geometry of a cubic Thue equation", Publ.Math.Debrecen 61/3-4(2002), p267-314.
- E.Bombieri, D.C.Hunt, A.J.van der Poorten, "Determinants in the study of Thue's method and curves with prescribed singularities", 1991, p1-13.
- Michael A.Bennett, "Lucas' square pyramid problem revisited", June 17, 2002, p1-8.
- Barry Mazur, Karl Rubin, "Elliptic curves and class field theory", ICM 2002, Vol.II, 1-3, p1-10.
- Roger E.Frye, "Finding 95800^4+217519^4+414560^4=422481^4 on the Connection Machine", Nov. 9, 1999, p1-11.
- J.E.Cremona, P.Serf, "Computing the rank of elliptic curves over real quadratic number fields of class number 1", May 20, 1996, p1-22.
- J.E.Cremona, "Efficient solution of rational conics", April 11, 2000, p1-30.
- J.E.Cremona, "Higher descents on elliptic curves", Aug, 1997, p1-9.
- J.E.Cremona, "On the computation of Mordell-Weil and 2-Selmer group of elliptic curves", p1-11.
- J.E.Cremona, "Modular symbols and the computation of modular ellipric curves", p1-31.
- J.E.Cremona, "Reduction of binary cubic and quartic forms", LMS J. Comput. Math. 2(1999), p62-94.
- Joseph H.Silverman, "Computing rational points on rank 1 elliptic curves via L-series and canonical height", May 1, 1996, p1-18.
- Lev A.Borisov, Paul E.Gunnells, Sorin Popescu, "Elliptic functions and equations of modular curves", May 22, 2000, p1-15.
- Ian Caines, "Reductions of curves mod p and Nagell-Lutz", Nov. 7, 2000, p1-3.
- Brain Osserman, "Heegner's argument", p1-6.
- F.Bertault, O.Ramar\'e, P.Zimmermann, "On sums of seven cubes", p1-8.
- Joseph H.Silverman, "A survey of the arithmetic theory of elliptic curves", p17-42.
- Robert P.Langlands, "Representatation Theory Its rise and its role in number theory", Proceedings of the Gbbs Symposium, AMS, 1990, p1-34.
A9
- Charles Denis Xavier, "Primality testing", p1-18.
- 伊豆 哲也, 野呂 正行, 横山 和弘, "モジュラー多項式の計算", SCIS'98-1.1.A, 1998, p1-8.
- 伊豆 哲也, "Risa/Asirによるmodular polynomialの計算", 京都大学数理解析研究所講究録, 1996, p1-8.
- Wenzhi Luo, Dinakar ramakrishman, "Determinations of modular elliptic curves by heegner points", p1-7.
- Jorge Jimenez-Urroz, Tonghai Yang, "Heegner zeros of theta functions", p1-16.
- Jan Nekov\'ar, Norbert Schappacher, "On the asymptotic behaviour of heegner points", p1-7.
- V.Vatsal, "Rank-one twists of a cetain elliptic curve", June 18, 1999, p1-6.
- 梅垣 敦紀, "On genus 2 curves with complex multiplication", p1-10.
- Hans-Georg R\"uck, Ulrich Tipp, "Heegner points and L-series of automorphic cusp forms of Drinfeld type", p1-78.
- Steven D.Galbraith, "Rational points on X_0^+(N) and quadratic Q-curves", July 20, 2000, p1-12.
- Bjorn Poonen, "An explicit algebraic family of genus-one curves violating the Hasse Principle", March 18, 2000, p1-10.
- Bjorn Poonen, "Computing torsion points on curves", March 26, 2001, p1-21.
A10
- N.J.A.Sloane, "My favorite integer sequences", p1-28.
- Andrew Baker, "Elliptic cohomology, p-adic modular forms and Atkin;s operator U_p", p1-6.
- Jean-Marc Souveignes, "Computing l-isogenies with the p-torsion", p1-7.
- Ed Schaefer, "Rational points on algebraic curves Lecture I", Jan. 22, 1999, p1-6.
- Ed Schaefer, "Rational points on algebraic curves Lecture II", Feb. 5, 1999, p1-5.
- Ed Schaefer, "Rational points on algebraic curves Lecture III", Feb. 19, 1999, p1-5.
- Ed Schaefer, "Rational points on algebraic curves Lecture IV", March 5, 1999, p1-6.
- Ed Schaefer, "Rational points on algebraic curves Lecture V", March 19, 1999, p1-5.
- Ed Schaefer, "Tamagawa numbers", p1-10.
- Ed Schaefer, "N\'eron models", p1-5.
- Ed Schaefer, "Can the 5-part of the Shafarevich-Tate group of an elliptic curve get arbitarily large", June 28, 2000, p1-4.
- E.Victor Flynn, Joseph L.Wetherell, "Finding rational pints on bielliptic genus 2 curves", 1999, p1-19.
- Guido Kings, "The Tamagawa number conjecture for CM elliptic curves", May 2000, p1-62.
- E.Victor Flynn, Joseph L.Wetherell, "Covering collection and a challenge problem of Serre", p1-11.
A11
- Stephen S.Kudla, Michael Rapoport, Tonghai Yang, "Derivatives of Eisenstein series and Faltings height", p1-88.
- J.H.Coates, S.Howson, "Euler characterristics and elliptic curves II", p1-59.
- Jiu-Kang Yu, "A class number relation over function fields", Journal of Number Theory, Vol.54, No.2, 1995, p318-340.
- Amnon Besser, "On the finiteness of III for motives associated to modular forms", Feb. 1, 1996, p31-46.
- Tsuneo Arakawa, Siegfied B\"ocherer, "Vanishing of certain spaces of elliptic modular forms and some applications", p1-30.
- Bas Edixhoven, "Minimal resolution and stable reductions of X_0(N)", Nov. 18 ,1998, p1-34.
- Bas Edixhoven, Anfrei Yafaev, "Subvarieties of Shimura varaieties", May 29, 2001, p1-26.
- C.Khare, C.S.Rajan, "Heegner points of large conductors", 1991, p1-5.
- V.Vatsal, "Uniform distribusion of Heegner points", Oct. 31, 2001, p1-47.
A12
- H.Cohen, "Computaional class field theory", p1-58.
- K.Rubin, A.Silverberg, "A report of Wiles' Cambridge lectures", 1991, p1-24.
- Henri Darmon, Lo\"ic Merel, "Winding quotients and some variants of Fermat's Last Theorem", Jan. 5, 2001, p1-26.
- Seigo Arita, "Weil descent of elliptic curves over finite fields of cahacteristic three", p1-11.
- Joseph H.Silverman, "The space of rational maps on P^1", July 30, 1996, p1-30.
- Joseph H.Silverman, "The average rank of an algebraic family of elliptic curves", July 1, 1997, p1-15.
- Joseph H.Silverman, "A bound for the Mordell-Weil rank of an elliptic surface after a cyclic base extension", June 3, 1997, p1-21.
- Eva Bayer-Fluckiger, "Classical group and the Hasse Principles", p1-2.
- R.H.Buchholz, "Triangles with three rational medians", p1-15.
- Hans-Georg R\"uck, "L-series, Heegner points and Drinfeld modular curves", p1-3.
- G.Donald Allen, "Algebra and Number Theory", Oct. 22, 2000, p1-35.
- 高島 克幸, "主偏極CMアーベル曲面の井草不変量が満たす類多項式について", Jan 27, 2001, p1-27.
- Hiroki Sumida, "Cyclotomic units, Gauss sums and Iwasawa invariants of certain real abelian fields", 2000, p1-10.
- Run\'e Schoof, "Algebraic curves and coding theory. Abuja 1990", Feb. 28, 2000, p1-38.
- 中川 仁, "楕円曲線について", Sep. 17, 1997, p1-14.
- A.Wiles, "The Birch and Swinnerton-Dyer Conjecture", p1-7.
A13
- Alfred J. van der Poorten, "On number theory and Kustaa Inkeri", p281-292.
- Bert van Geeman, Jaap Top, "A non-selfdual automorphic representation of GL_3 and a Galois representation", 1991, p1-7.
- Henri Darmon, "Heegner points, Heegner cycles, and congruences", May 23, 2000, p1-35.
- E.Victor Flynn, Franck Lepr\'evost, Edward F.Schaefer, William A.Stein, Michael Stoll, Joseph L.Wetherell, "Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves", June 21, 2000, p1-23.
- A.O.L.Atkin, F.Morain, "Elliptic curves and Primality Proving", Dec. 23, 1992, p1-45.
- F.Morain, "ECPP Comes Back", Apr. 20,1997, p103-108.
- Annette Fuber, Guido Kings, "Bloch-Kato conjecture and Main conjecture of Iwasawa Theory for Dirichlet Charactters", Dec. 22, 2000, p1-50.
- Ilan Vardi, "Archimedes' Cattile Problem", p1-16.
- Luis Manuel, Navas Vicente, "Supersingular prmes and p-adic L-functions", Pacific Journal of Math. Vol.198, No.2, 2001, p489-500.
A14
- John Cremona, "The arithmetic of elliptic curves", p1-13.
- John Cremona, "Classical invariants theory and 2-descent on elliptic curves", p0-14.
- Marc Hindry, Joseph Silverman, "Sur le nombre de points de torsion rationnels sur une courbe elliptique", p1-4.
- Joseph Silverman, "Divisibility of the specialization map for twists of Abelian varaieties", Preprint, June 14, 1996, p1-12.
- Joseph Silverman, "On the rank of elliptic curves", Feb. 4, 1999, p1-9.
- Joseph Silverman, "Low Complexity Multiplication in Rings", p1-20.
- Joseph Silverman, "On the distribution of integer points on cyrves of genus zero", Sep. 2, 1998, p1-7.
- Joseph Silverman, Joe Suzuki, "Elliptic curve Discrete Logarithms and the Index Calculus", p1-16.
- Joseph Silverman, "The Xendi calculus and the elliptic curve discrete logarithms problem [Preliminary Version]", Aug. 3, 1998, p1-33.
- John Cremona, "Modular forms and elliptic curves over imaginary quadratic fields", p1-12.
- John Cremona, "Computing periods of cusp forms and Modular elliptic curves", Experimental Mathematics, Vol.6, No.2, 1997, p97-107.
- John Cremona, "G13NUM: Number Theory Course Notes 2000", p1-45.
- John Cremona, "G1CRPC: Rational Points on Curves Course Notes 2001", p1-36.
- John Cremona, B.Mazur, "Visualizing elements in the Safarevich-Tate group", p1-23.
- K.R.Matthews, "The generalized 3x+1 mapping", Aug. 29, 2001, p1-23.
- Matthews Read, "Consequnces of the Riemann Hypothesis", Dec. 2002, p1-142.
A15
- Guy Henniart, "Congruent numbers, elliptic curves, and modular forms", p1-14.
- Lo\"ic Merel, "Arithmetic of elliptic curves and diophantine equations", p1-31.
- 佐藤 篤, "コンピュータによる楕円曲線の計算", Nov. 2002, p1-16.
- 佐藤 篤, "V\'eluの公式とその応用", p1-24.
- 佐藤 篤, "Rational poits on quadratic twists of an elliptic curves", p1-2.
- P.Gaudry, L.Kulesz, G.Matera, E\'.Schost, "Uniform bounds for the number of rational points of families of curves of genus 2", p1-10.
- Ramin Takloo-Bighash, "On distribution of rational points on elliptic curves", Oct. 17, 1999, p1-3.
- Masanari Kida, "Computing elliptic curves using KASH", Aug. 18, 2002, p1-22.
- Karl Rubin, "Right triangle and elliptic curves", p1-8.
- Tom Fisher, "Rational points on X(11) over Q(μ_11) via Galois equivariance of the Cassels-Tate pairing", April 11, 2001, p1-15.
- Serge Ochanine, "Elliptic Genera", July 1996, p1-7.
- Gerard van de Geer, Marcek van der Vlugt, "Constructing curves over finite fields with many points by solving linear equations", p1-6.
- H.Darmon, "Wiles' theorem and the arithmetic of ellitic curves", Nov. 19, 1998, p1-24.
- Gerd Faltings, "The proof of Fermat's Last Theorem by R.Taylor and A.Wiles", Notice of AMS, July 1995, p743-746.
- Kristian Gjosteen, "Hasse's theorem", Sep. 18, 2000, p1-13.
- 青木 昇, "楕円曲線のセルマー群について", p1-4.
- 田口 雄一郎, "p進数", p1-9.
- 田口 雄一郎, "Fermatの最終定理 -Wilesによる証明な解説", p1-40.
- 田口 雄一郎, "Mod p Galois表現について(特に像が可解の場合)", p1-9.
- 田口 雄一郎, "Fontaine-Mazur予想の紹介", p1-13.
- Jeff Achter, "On Computing the rank of elliptic curves", May 1992, p1-48.
- Karl Rubin, "Elliptic Curves with Complex Multiplication and the Conjecture of Birch and Swinnerton-Dyer", p1-68.
A16
- Josep Gonza\'lez, "On the j-invariants of the quadrtic Q-curves", 2000, p1-27.
- 菅 真紀子, "θ-合同数と楕円曲線", 2002, p1-104.
- Brain Osserman, "Heegner's Work and its applications", p1-30.
- Wenzhi Luo, Dinakar ramakrishman, "Determinations of modular elliptic curves by heegner points", Pacific Journal of Math. Vol.181, No.3, 1997, p251-258.
- Steven D.Galbraith, "Equations for Modular Curves", PhD-thesis, 1996, p1-91.
- Fedor Bogomolov, Yuri Tschinkel, "On curves correspondances", p1-10.
A17
- E.Kaltofen, "Factorization of Polynomials", p1-21.
- Mark Giesbrecht, "Efficient Parallel Solution of Sparse Systems of Linear Diophantine Equations", p1-10.
- Erich Kaltofen, "Computing Gratest Common Divisors ans Factorizarions in Quadratic Number Fields", p1-28.
- Erkay Sva\c s, Thomas A.Schmidt, \c Cetin K.Ko\c c, "Generationg elliptic cuves of prime order", p1-17.
- Noam D.Elkies, "The Klein Quartic in Number Theory", The Eightfold Way MSRI Publ. Vol.35, 1998, p51-101.
- Robert P.Langlands, "Where stands functionality today?", p1-11.
- Jan Nekov\'ar, "On the parity of ranks of Selmer groups II", Nov. 11, 2000, p1-7.
- Imin Chen, "On Siegel;s modular curve of level 5 and the class number one problem", Aug. 1, 1998, p1-15.
- H.Darmon, "Elliptic curves and p-adic uniformisation", Feb. 3, 1999, p1-19.
- Franz Lemmermeyer, "The Euclidean Algorithms in Algebraic Number Fields", 1991, p1-53.
- Franz Lemmermeyer, "Ideal Class Group of Cyclotomic Number Fields I", 1991, p1-11.
- Franz Lemmermeyer, "Ideal Class Group of Cyclotomic Number Fields II", 1991, p1-12.
- Malcolm Harper, "A proof that Z[\sqrt{14}] is a Euclidean Domain", July 2000, p1-66.
- 伊豆 哲也, "LLLアルゴリスムについて(Ver. 0.1)", May 7, 2002, p1-15.
- 伊豆 哲也, "NTRU Signature Scheme(NSS)について", Oct. 16, 2001, p3-12.
- 伊豆 哲也, "格子理論入門", 2002, p1-24, "立教大学数学科で2002年度に開講された[代数学緒論2]の講義ノートを元に作成したもの".
A18
- Alice Gee, Peter Stevenhagen, "Generaing class fields using Shimura reciprocity", 1991, p1-12.
- Hilmar Hauer, "Modular curves and Heegner points", Oct. 16, 2001, p1-7.
- T.Schmidt, "MTH 649. Elliptic Curves: Theory and appliation", June 2, 1999, p1-32.
- Gerhard Frey, Michael M\"uller, Hans0Georg Ru\"ck, "The Tate pairing and discrete logarithm applied to elliptic curve cryptosystems", Oct. 7, 1998, p1-5.
- Alexandru Ghitza, "Modular curves and Heegner points", Feb. 15, 2000, p1-6.
- Igor Dolgachev, "Lecture on Modular Forms", Fall 1997/98, p1-150.
- H.Darmon, "The equation x^4-y^4=z^p", May 23, 2000, p1-5.
- Bjorn Poonen, "Elliptic Curves", March 30, 2001, p1-21.
- Noam D.Elkies, "Rational points near curves and small nonzero |x^3-y^2| via latttice reduction", May 14, 2000, p1-31.
- Clemens Heuberger, "Parametrized Thue equations ---- A survey", May 3, 2002, p1-10.
- Bjorn Poonen, "Computaional aspect of curves of genus at least 2", April 10, 1996, p1-21.
- Roel J.Stroeker, Benjamin M.M. de Weger, "On elliptic Diophantine equations that defy Thue's method: The case of the Ochoa curve", Experimental Math., Vol.3, No.3, 1994, p209-220.
- Istv\'an Ga\'al, Attila Peth\"o, Michael Pohst, "On the resolution of index form equations in dihedral quatic number fields", Experimental Math., Vol.3, No.3, 1994, p243-254.
- Harvey E.Rose, "On some elliptic curves with large Sha", Experimental Math., Vol.9, No.1, 2000, p85-89.
- Bruce Hunt, "Nice modular varieties", Experimental Math., Vol.9, No.4, 2000, p613-622.
- Sylvain Duquesne, "Integral points on elliptic curves defined bt simplest cubic fields", Experimental Math., Vol.10, No.1, 2001, p91-102.
- Chrisophe Delaunay, "Heuristics on Tate-Shafareutch group of elliptic curves defined over Q", Experimental Math., Vol.10, No.2, 2001, p191-196.
- Nicholas F.Rogers, "Rank computations for the congruent number elliptic curves", Experimental Math., Vol.9, No.4, 2000, p591-594.
- Benjamin W.W. de Weger, "Solving elliptic Diophantine equations avoiding Thue equations and elliptic logarithms", Experimental Math., Vol.7, No.3, 1998, p243-256.
- Andrew Bewmner, "On aroithmetic progression on elliptic curves", Experimental Math., Vol.8, No.4, 1999, p409-413.
- R.J.Stroeker, N.Tzanakis, "Computing all integer solutions of a genus 1 equation", p1-20.
- Maurice Mignotte, Attila Peth\"o, Ralf Roth, "Complete solutions of a family of quartic Thue and index form equations", Math. of Comput., Vol.65, No.213, 1996, p341-354.
- Paulo S.L.M.Barreto, Ben Lynn, Michael Scott, "Constructing elliptic curves with prescribed embedding degrees", p1-11.
- ???, "Three lectures about the arithmetic of elliptic curves", p1-33.
- P.Corvaja, U.Zannier, "On integral points on surfaces", p1-14.
- Masato Kuwata, Jaap Top, "A singular K3 surface related to sums of consecutive cubes", Oct. 1999, p1-16.
- Keith Matthews, "The Diophantine equation x^2-Dy^2=N, D > 0", p1-9.
- Franz Lemmermeyer, "Unramified quaternion extensions of quadratic number fields", Nov. 11, 2001, p1-14.
A19
- J.Coates, G.Poitou, "News about Roots of Unity", Nov. 17, 2001, p1-17.
- Franz Lemmermeyer, "A note on P\'epin's counter examples to the Hasse principle for curves of genus 1", Nov. 11, 2001, p1-12.
- Franz Lemmermeyer, "On Tate-Shafavrevich groups of some elliptic curves", p1-13.
- Jean-Pierre Serre, "An interpretation of some congruences concerning Ramanujan's τ-function", Nov. 17, 2001, p1-15.
- Hans-Georg Ru\"ck, Ulrich Tipp, "Heegner points and L-series of automorphic cusp forms of Drinfeld type", Docmenta Math. Vol.5, 2000, p365-444.
- Franz Lemmermeyer, "Kuroda's class number formula", p1-14.
- Franz Lemmermeyer, "Rational quartic reciprocity", p1-4.
- Jacques V\'elu, "Galois groups atached to points of finite order on elliptic curves over number fields (D'Apr\'es Serre)", p1-8.
- Franz Lemmermeyer, "Contruction of Hilbert 2-class fields", p1-6.
- Franz Lemmermeyer, Norbert Schappacher, "Introduction to the English Edition of Hilbert's Zahlbericht", Nov. 11, 2001, p1-12.
- Ren\'e Schoof, "Counting points on elliptic curves over finite fields", Journal de Th\'eorie de Nombres de Bordeau 7(1995), p219-215.
- Fran\c cois Morain, "Implementation of the Schoof-Atkin-Elkies Algorithm", March 7, 1994, p129-132.
- Bas Edixhoven, "On N\'eron models, divisors and modular curves", March 26, 1999, p1-27.
- Renaud Lifchitz, "A geberalization of the Korselt's criterion nested Carmichael numbers", March, 2002, p1-3.
- Ricard G.E.Pinch, "The Carmichael numbers up to 10^16", March 18, 1998, p1-9.
A20
- I.Connell, "Elliptic Curve Handbook", 1997, p101-166(Chap.1),p201-281(Chap.2),p301-384(Chap.3),p401-441(Chap.4),p501-543(Chap.5).
A21
- William F.Hammond, "Fermat's Last Theorem After 356 Years", Oct 22, 1993, p1-26.
- Erich Kaltofen, Noriko Yui, "Explicit Construction of the Hilbert Class Fields of Imaginary Quadratic Fields by Integer Lattice Reduction", 1985, p149-190.
- J.S.Milne, "Modular Functions and Modular Forms", 1997, p1-126.
- Berndt E.Schwerdtfeger, "The Zeta-function of x^4+y^4+z^4=0", Jan 27, 2003, p1-11.
- Shu-Leung Tang, "Congruences between Modualr Forms, Cyclic Isogenies of Modular Elliptic curves, and Inetgrality of p-adic L-function", Transactions of AMS, Vol.349, No.2, 1997, p837-856.
- C.L.Stewart, "Second thoughts on some topics from Diophantine approximaion and anaytic number theory", p1-20.
- Richard Taylor, "Galois Representations", p1-36.
- Richard Taylor, "Galois Representations", 2000, p1-41.
- Richard Taylor, "On congruences between modular forms", June 1988, p1-138.
- Richard Taylor, Andrew Wiles, "Ring Theoretic Properties of Certain Hecke Algebras", Oct 7, 1994, p1-22.
- Henri Darmon, "The calculation of periods on $H_p times H$ and Heegner points attached to real quadratic fields: a pregress report", Feb 9, 2001, p1-14.
A22
- Ken McMurdy, "A Splitting Criterion for Galois Representations Associated to Exceptional Modular Forms", Sep 20, 2001, p1-58.
- Noam D.Elkies, "Explicit modular fowers", p1-10.
- Noam D.Elkies, "Shimura Curve Computations", p1-48.
- Keith Matthews, "The Diophantine equation ax^2+bxy+cy^2=N, D=b^2-4ac>0", 1991, p1-12.
- Steven D.Galbraith, "Rational Points on $X^{+}_0(N)$ and quadratic Q-curves", July 20, 2000, p1-12.
- William Stein, "Lecture 32: Fermat's Last Theorem and Mpodularity of Elliptic Curves", 2001, p1-4.
- Ernst Kani, "Fermat's Last Theorem", 1996, p1-8.
- Enrique Gonz\'alez-Jim\'enez, Joep Gonz\'alez, "Modular curves of genus 2", Sep 22, 2002, p1-22.
- Yves Martin, Ken Ono, "Eta-Quotients and elliptic curves", Proceeding of the AMS, Vol.125, No.11, 1997, p3169-3176.
- David R.Kohel, "Computing modular curves via quaternions", Jan, 1997, p1-21.
- David Joyner, Salahoddin Shokranian, "Remarks on codes from modular curves: MAPLE applications", Aug 12, 1999, p1-29.
- Henri Darmon, "Serre's Conjecture", Nov 25, 1998, p1-30.
- Alice Gee, "Class invariants by Shimura's reciprocity law", Journal de Th\'eorie des Nombres de Bordeau 11, 1999, p45-72.
A23
- A.Enge, F.Marain, "Computing invariants for class fields of imaginary quardratic fields", p1-15.
- J.S.Milne, "Canonical models for modular curves", 2002, p1-23.
- Brain Osserman, "Kolyvagin Seminar: Overview and background material", p1-3.
- Victor Rotger, "On the group of automorphisms of Shimura curves and applications", Composititoin Math. 131(2002), p1-18.
- Henri Darmon, "Refined class number formulas for derivatives of L-series", 1991, thseis, p1-74.
- Pete L.Clark, "Lecture Notes on Eichler-Shimura Theory", 2000, p1-8.
- ???, "The AGM-X_0(N) Heegner Point Lifting Algorithm and Elliptic Curtve Point Counting", p1-12.
- Michael A. Bennett, K\'alma\'n Gy\"oy, \'Akos Pint\'er, "On the Diophantine Equation 1^k+2^k+...+x^k=y^n", 1991, p1-20.
- Yann Bugeaud, T. N. Shorey, "On the Diophantine Equation (x^m-1)/(x-1)=(y^n-1)/(y-1)", Pacific Journal of Mathematics, Vol.207, NO.1, 2002, p61-75.
- Yann Bugeaud, "On the Diophantine Equation a(x^n-1)/(x-1)=y^q", 1991, p1-5.
- Felix Lazerbnik, "On systems of linear Diophantine Equations", p1-6.
- 千田 雅隆, "類体論の概要", 2002, p1-8.
- 千田 雅隆, "Rank of quadratic twists of elliptic curves", 2002, p1-6.
- 千田 雅隆, "Products of Special Values of Twist L-functions and its Applications", 2003, preprint, p1-15.
- M. A. Bennett, "Simultaneous approximation to pairs of algebraic numbers", Canadian Mathematical Society Proceedings, Volume 15 (1995), 55-65.
- M. A. Bennett, "Simultaneous rational approximation to binomial functions", Trans. Amer. Math. Soc. 348 (1996), 1717-1738.
- M. A. Bennett, "Effective measures of irrationality for certain algebraic numbers", J. Austral. Math. Soc. 62 (1997), 329-344.
- M. A. Bennett, N. P. Dummigan, T. D. Wooley, "The representation of integers by binary additive forms", Compositio Math. 111 (1998), 15-33.
- M. A. Bennett, "Explicit lower bounds for rational approximation to algebraic numbers", Proc. London Math. Soc. 75 (1997), 63-78.
- M. A. Bennett, "Solving norm form equations via lattice basis reduction", Rocky Mountain Journal of Mathematics 26 (1996), 815-837.
- M. A. Bennett, "Pillai's conjecture revisited", p1-6.
- M. A. Bennett, "Products of consecutive integers", p1-11.
- M. A. Bennett, "On some exponential equations of S.S. Pillai", Canad. J. Math. 53 (2001), 897-922.
- M. A. Bennett, B. M. M. de Weger, "On the Diophantine equation $|ax^{n}-by^{n}|=1$", Math. Comp. 67 (1998), 413-438.
- M. A. Bennett, "On the representation of unity by binary cubic forms", Trans. Amer. Math. Soc. 353 (2001), 1507-1534.
- M. A. Bennett, P. G. Walsh, "Simultaneous quadratic equations with few or no solutions", Indag. Mathem. 11 (2000), 1-12.
- 平之内 俊郎, "Tateのアルゴリズム", p1-8.
- 平之内 俊郎, "岩澤理論", p1-35.
- Ryotaro Okazaki, "Geometry of a Quartic Thue Equation", Dec. 01, 2001, p1-16.
- Yann Bugeuad, "On some exponential Diophantine equations", 1991, p1-6.
A24
- Takaaki Kagawa, "Elliptic curves with everywhere goood reduction over real quadraric fields", March 1998, p1-60.
- Sylavain Duquesne, "Th\`ese", 2001, p1-156.
- Samir Siksek, John Cremona, "On The Diophantine Equation x^2+7=y^m", 2000, p1-7.
- Andrej Dujella, "Diophantine m-tuples and elliptic curves", J.de Th\'eorie des Nombres de Bordeau 13(2001), p111-124.
- Jordan S.Ellenberg, "Q-curves and Galois representations", 2003, p1-10.
- Gary Walsh, "A note on a theorem of Ljunggren and the Diophantine equations x^2-kxy^2+y^4=1,4", Arch. Math. 73(1999), p119-125.
- J.H.E.Cohn, "The Diophantine Equation x^4+1=Dy^2",Math. of Comp, Vol.66(1997), No.219, p1347-1351.
- Michael A. Bennett, Gary Walsh, "Simultaneous quadratic quations with few or no solutions", 1999, p1-10.
- M. A. Bennett, "On consecutive integers of the form $ax^2, by^2$ and $cz^2$", Acta Arith. 88 (1999), 363-370.
- Michael A. Bennett, Gary Walsh, "The Diophantine Equation b^2X^4-dY^2=1", 1991, p1-10.
- William C.Jagy, Irving Kaplansky, "Sums of Squares, Cubes, and Higher Powers", Experimental Math., Vol.4(1995), No.4, p169-173.
- Samir Siksek, "Sieving for rational points on hyperelliptic curves", Math. of Computation, Vol. 70, No.236, 2001, p1661-1674.
- Nils Bruin, "Chabauty methods and covering techinques applied to generalized Fermat equations", 1972, p1-79.
- Nils Bruin, "Chabauty methods using covers on curves of genus 2", 1999, p1-14.
- Nils Bruin, "Chabauty methods using covers", 1999, p1-22.
- Jordan S. Ellenberg, "Congruence ABC implies ABC", 25 March, 1999, p1-4.
A25
- Jordan S. Ellenberg, "Galois representations attached to Q-curves and the generalized Fermat equation A^4+B^2=C^p", 22 Jul, 2003, p1-20.
- Le Maohua, "On the Diophantine Equation x^2+D=y^n", Acta Math. Sinica, Vol.40, No.6, 1997, p839-844, Chinese.
- Franz Lemmermeyer, Attila Peth\"o, "Simplest Cubic Fields", p1-6.
- Attila Peth\"o, "Diophantine properties of linear recursive sequences I", July 12, 2003, p1-16.
- Attila Peth\"o, "Diophantine properties of linear recursive sequences II", Acta Math, 17(2001), p81-96.
- Clemens Fuchs, Attila Peth\"o, Robert F. Ticky, "On the Diophantine equation G_n(x)=G_m(P(x))", July 29, 2002, p1-25.
- Jennifer Balakrishnan, "4-descent on the elliptic curve y^2=x^3+7823", May 17, 2003, p1-8.
- Michael Stoll, "Explicit 4-descent on an elliptic curve", Jan 22, 2002, p1-6.
- Grigor Grigorov, Jordan Rizov, "Heights on Elliptic Curves and the Diophantine Equation x^4+y^4=cz^4", Jan 10, 1998, p1-9.
- Garikai Campbell, Edray Herber Goins, "Heron Triangles, Diophantine Problems and Elliptic Curves", 2000, p1-15.
- David J. Rusin, "Rational Triangles with Equal Area", 1998, New York J. Math. 4, p1-15.
- Edray Herber Goins, Davin Maddox, "Heron Triangles via Elliptic Curves", 1991, p1-11.
- Garikai Campbell, Edray Herber Goins, "Explicit Descent via 4-isogeny on an elliptic curve", 2000, p1-6.
- Edray Herber Goins, "A Ternary Algebra with Applications to Binary Quadratic Forms", p1-6.
- Edray Herber Goins, Alain Togbe, "Pythagorean Quarduplets", 1991, p1-7.
- Edray Herber Goins, "Ma 105: Elliptic Curves", 2002, p1-115.
B1
- Michael E.Pohst, "KASH User's Guide", Jan. 30, 1999, p1-400.
B2
- Michael E.Pohst, "KASH User's Guide", Jan. 30, 1999, p401-835.
B3
- SIMATH development group, "SIMATH Manual: An Introduction to the Compter Algebra System SIMATH and the calculator SIMCALC", 2002, p1-145.
- Horst G. Zimmer, "SIMATH - a computer algebra system for number theoretic applications", p1-48.
- Horst G. Zimmer, "Basic Algorithms for elliptic curves", p1-27.
- Tetsushi Matsui, Mizuko Abe, Daisuke Kobayashi, Ken Nakamula, "SIMATH - Recent Developments in TMU", 6 May, 2002, p1-2.
B4
- 木田 雅成, "TECC-KASHによる楕円曲線の計算", Nov. 22, 2000, p1-13.
- John Voight, "Computing with elliptic curves: Implementations", Sep. 20, 2000, p1-13.
- Bill Allombert, Ariel Pacetti, "An introduction to gp2c", May 19, 2002, p1-10.
- C.Batut, K.Belabas, B.Bernardi, H.Cohen, M.Olibier, "A Tutorial for PARI/GP", 2000, Version 2.1.1, p1-226.
B5
- Joseph H.Silverman, "Elliptic Curve Calculator Version 2.0", July 25, 1992, p1-20.
- William A.Stein, "HECKE: The Modular Forms Calculator", p1-6.
- Masayuki Noro, Takeshi Shimoyama, Taku Takeshima, "Asir User's Manual, Edition 4.5 for Asir-20010313", March 2001, p1-158.
- 山口 和紀, 五十嵐 淳, "情報システム科学実習II 第1回 授業概要", Oct. 10, 2001, p1-6.
- 山口 和紀, 五十嵐 淳, "情報システム科学実習II 第2回 基本データ型,変数の宣言,簡単な関数", Oct. 17, 2001, p1-16.
- 山口 和紀, 五十嵐 淳, "情報システム科学実習II 第3回 再帰による繰り返し", Oct. 24, 2001, p1-16.
- 山口 和紀, 五十嵐 淳, "情報システム科学実習II 第4回 高階関数,多相性,多相的関数", Nov. 7, 2001, p1-15.
- 山口 和紀, 五十嵐 淳, "情報システム科学実習II 第5回 再帰的データ構造: リスト", Nov. 14, 2001, p1-13.
- 山口 和紀, 五十嵐 淳, "情報システム科学実習II 第6回 レコード型/ヴァリアント型とその応用", Nov. 21, 2001, p1-15.
- 山口 和紀, 五十嵐 淳, "情報システム科学実習II 第7回 参照,例外処理,入出力", Nov. 28, 2001, p1-11.
- 山口 和紀, 五十嵐 淳, "情報システム科学実習II 第8回 モジュールとバッチコンパイル システムプログラミング入門", Dec. 5, 2001, p1-14.
- 山口 和紀, 五十嵐 淳, "情報システム科学実習II 第9回 ファンクター", Dec. 12, 2001, p1-11.
- 山口 和紀, 五十嵐 淳, "情報システム科学実習II 第10回 LOGOインタプリタの作成", Jan. 9, 2002, p1-13.
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