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Invariants des courbes de Frey-Hellegouarch et grands groupes de Tate-Shafarevich

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Warianty tytułu
Języki publikacji
FR
Abstrakty
Twórcy
  • Fb 9, Mathematik, Universität des Saarlandes, Postfach 15 1150, D-66041 Saarbrücken, Germany
Bibliografia
  • [1] A. O. L. Atkin and J. Lehner, Hecke operators on Γ₀(m), Math. Ann. 185 (1970), 134-160.
  • [2] C. Batut, D. Bernardi, H. Cohen and M. Olivier, PARI-GP, a computer system for number theory, Version 2.0, ftp://megrez.math.u-bordeaux.fr/pub/pari/.
  • [3] R. Bölling, Die Ordnung der Schafarewitsch-Tate-Gruppe kann beliebig groß werden, Math. Nachr. 67 (1975), 157-179.
  • [4] J. W. S. Cassels, Arithmetic on curves of genus 1. VI. The Tate-Šafarevič group can be arbitrarily large, J. Reine Angew. Math. 214/215 (1964), 65-70.
  • [5] H. Cohen, A Course in Computational Algebraic Number Theory, Grad. Texts in Math. 138, Springer, Berlin, 1993.
  • [6] I. Connell, APECS, Version 4.36 1998, ftp://math.mcgill.ca/pub/apecs/.
  • [7] J. Cremona, Algorithms for Modular Elliptic Curves, Cambridge Univ. Press, Cambridge, 1992.
  • [8] P. Deligne, Les constantes des équations fonctionnelles des fonctions L, in: Antwerp II: Modular Functions of One Variable, Lecture Notes in Math. 349, Springer, 1973, 501-597.
  • [9] F. Diamond, On deformation rings and Hecke rings, Ann. of Math. 144 (1996), 137-166.
  • [10] F. Diamond and K. Kramer, Modularity of a family of elliptic curves, Math. Res. Lett. 2 (1995), 299-304.
  • [11] G. Frey, Some aspects of the theory of elliptic curves over number fields, Exposition. Math. 4 (1986), 35-66.
  • [12] J. Gebel and H. G. Zimmer, Computing the Mordell-Weil group of an elliptic curve over ℚ, in: Elliptic Curves and Related Topics, CRM Proc. Lecture Notes 4, Amer. Math. Soc., 1994, 61-83.
  • [13] D. Goldfeld and D. Lieman, Effective bounds on the size of the Tate-Shafarevich group, Math. Res. Lett. 3 (1996), 309-318.
  • [14] D. Goldfeld and L. Szpiro, Bounds for the order of the Tate-Shafarevich group, Compositio Math. 97 (1995), 71-87.
  • [15] B. H. Gross, Kolyvagin's work on modular elliptic curves, in: L-functions and Arithmetic (Durham, 1989), Cambridge Univ. Press, 1991, 235-256.
  • [16] D. Husemöller, Elliptic Curves, Grad. Texts in Math. 111, Springer, Berlin, 1986.
  • [17] W. Kohnen and D. Zagier, Values of L-series of modular forms at the center of the critical strip, Invent. Math. 64 (1981), 175-198.
  • [18] V. A. Kolyvagin, Finiteness of E(ℚ) and Ш(E/ℚ) for a subclass of Weil curves, Math. USSR-Izv. 32 (1989), 523-541.
  • [19] K. Kramer, A family of semistable elliptic curves with large Tate-Shafarevitch groups, Proc. Amer. Math. Soc. 89 (1983), 379-386.
  • [20] D. S. Kubert, Universal bounds on the torsion of elliptic curves, Proc. London Math. Soc. 33 (1976), 193-237.
  • [21] S. Lang, Conjectured diophantine estimates on elliptic curves, in: Progr. Math. 35, Birkhäuser, 1983, 155-172.
  • [22] A. K. Lenstra, H. W. Lenstra and L. Lovász, Factoring polynomials with rational coefficients, Math. Ann. 261 (1982), 515-534.
  • [23] L. Mai and M. R. Murty, A note on quadratic twists of an elliptic curve, in: Elliptic Curves and Related Topics, CRM Proc. Lecture Notes 4, Amer. Math. Soc., 1994, 121-124.
  • [24] Y. Manin, Cyclotomic fields and modular curves, Russian Math. Surveys 26 (1971), 7-78.
  • [25] A. Nitaj, Détermination de courbes elliptiques pour la conjecture de Szpiro, Acta Arith. 85 (1998), 351-376.
  • [26] A. Nitaj, Tables of good abc-examples, preprint, Saarbrücken, 1997.
  • [27] C. S. Rajan, On the size of the Shafarevich-Tate group of elliptic curves over function fields, Compositio Math. 105 (1997), 29-41.
  • [28] D. E. Rohrlich, Galois theory, elliptic curves, and root numbers, ibid. 100 (1996), 311-349.
  • [29] K. Rubin, Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication, Invent. Math. 89 (1987), 527-560.
  • [30] J. H. Silverman, The Arithmetic of Elliptic Curves, Grad. Texts in Math. 106, Springer, Berlin, 1986.
  • [31] Simath Group, SIMATH, a computer algebra system, Version 4.2, Saarbrücken, 1998, ftp://ftp.math.uni-sb.de:/pub/simath.
  • [32] B. M. M. de Weger, A+B=C and big Ш's, Quart. J. Math. Oxford Ser. (2) 49 (1998), 105-128.
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