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1996 | 77 | 2 | 157-171
Tytuł artykułu

On a characterization of Shimura's elliptic curve over ℚ(√37)

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
77
Numer
2
Strony
157-171
Opis fizyczny
Daty
wydano
1996
otrzymano
1995-06-23
poprawiono
1996-02-25
Twórcy
  • Department of Mathematics, The Johns Hopkins University, Baltimore, Maryland 21218, U.S.A.
  • Department of Mathematical Sciences, Yamagata University, Yamagata, 990 Japan
Bibliografia
  • [1] B. J. Birch and W. Kuyk (eds.), Modular Functions of One Variable IV, Lecture Notes in Math. 476, Springer, 1975.
  • [2] W. Casselman, On abelian varieties with many endomorphisms and a conjecture of Shimura's, Invent. Math. 12 (1971), 225-236.
  • [3] J. E. Cremona, Modular symbols for Γ₁(N) and elliptic curves with everywhere good reduction, Math. Proc. Cambridge Philos. Soc. 111 (1992), 199-218.
  • [4] J. E. Cremona, Algorithms for Modular Elliptic Curves, Cambridge University Press, 1992.
  • [5] P. Deligne et M. Rapoport, Les schémas de modules de courbes elliptiques, in: Modular Functions of One Variable III, Lecture Notes in Math. 349, Springer, 1973, 143-316.
  • [6] O. Hemer, On the Diophantine equation y²+k=x³, doctoral dissertation, Uppsala, 1952.
  • [7] F. Klein und R. Fricke, Vorlesungen über die Theorie der elliptischen Modulfunktionen II, Teubner, 1892.
  • [8] A. P. Ogg, Diophantine equations and modular forms, Bull. Amer. Math. Soc. 81 (1975), 14-27.
  • [9] A. Pethö and B. M. M. de Weger, Products of prime powers in binary recurrence sequences. Part I, The hyperbolic case, with an application to the generalized Ramanujan-Nagell equation, Math. Comp. 47 (1986), 713-727.
  • [10] R. G. E. Pinch, Elliptic curves over number fields, doctoral dissertation, Oxford University, 1982.
  • [11] K. A. Ribet, Endomorphisms of semi-stable abelian varieties over number fields, Ann. of Math. 101 (1975), 555-562.
  • [12] B. Setzer, Elliptic curves with good reduction everywhere over quadratic fields and having rational j-invariant, Illinois J. Math. 25 (1981), 233-245.
  • [13] G. Shimura, Introduction to the Arithmetic Theory of Automorphic Functions, Publ. Math. Soc. Japan 11, Iwanami Shoten and Princeton University Press, 1971.
  • [14] G. Shimura, Class fields over real quadratic fields and Hecke operators, Ann. of Math. 95 (1972), 130-190.
  • [15] G. Shimura, On the factor of the Jacobian variety of a modular function field, J. Math. Soc. Japan 25 (1973), 523-544.
  • [16] K. Shiota, On the explicit models of Shimura's elliptic curves, J. Math. Soc. Japan 38 (1986), 649-659.
  • [17] J. H. Silverman, The Arithmetic of Elliptic Curves, Grad. Texts in Math. 106, Springer, 1986.
  • [18] R. P. Steiner, On Mordell's equation y²-k=x³: A problem of Stolarsky, Math. Comp. 46 (1986), 703-714.
  • [19] N. Tzanakis and B. M. M. de Weger, On the practical solution of the Thue equation, J. Number Theory 31 (1989), 99-132.
  • [20] N. Tzanakis and B. M. M. de Weger, How to explicitly solve a Thue-Mahler equation, Comp. Math. 84 (1992), 223-288; Corrections 89 (1993), 241-242.
  • [21] M. J. Vélu, Isogénies entre courbes elliptiques, C. R. Acad. Sci. Paris Sér. A 273 (1971), 238-241.
  • [22] M. Waldschmidt, A lower bound for linear forms in logarithms, Acta Arith. 37 (1980), 257-283.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-aav77i2p157bwm
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