Tate-Shafarevich groups of the congruent number elliptic curves

• Autorzy: Ken Ono
• Języki publikacji: EN

Kategorie tematyczne

• 11G40: L -functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1997
• Tom: 81
• Numer: 3
• Strony: 247-252

Daty

wydano

1997

otrzymano

1996-10-15

poprawiono

1997-04-09

Twórcy

autor

Ken Ono

• School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540, U.S.A.

Bibliografia

• [B-E-W] B. C. Berndt, R. J. Evans and K. S. Williams, Gauss and Jacobi Sums, Wiley, to appear.
• [C] J. E. Cremona, Algorithms for Elliptic Curves, Cambridge Univ. Press, 1992.
• [D] L. E. Dickson, History of the Theory of Numbers, Vol. 3, G. E. Strechert & Co., 1934.
• [J] N. Jochnowitz, Congruences between modular forms of half integral weights and implications for class numbers and elliptic curves, preprint.
• [M-O] Y. Martin and K. Ono, Eta-quotients and elliptic curves, Proc. Amer. Math. Soc., to appear.
• [O-S] K. Ono and C. Skinner, Fourier coefficients of half-integral weight modular forms mod l, preprint.
• [R] K. Rubin, Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication, Invent. Math. 89 (1987), 527-560.
• [S] J. Silverman, The Arithmetic of Elliptic Curves, Springer, New York, 1986.
• [T] J. B. Tunnell, A classical Diophantine problem and modular forms of weight 3/2, Invent. Math. 72 (1983), 323-334.