Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Some conjectures on elliptic curves over cyclotomic fields

Authors: D. Goldfeld and C. Viola
Journal: Trans. Amer. Math. Soc. 276 (1983), 511-515
MSC: Primary 12A70; Secondary 10H10
MathSciNet review: 688958
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give conjectures for the mean values of Hasse-Weil type $ L$-functions over cyclotomic fields. In view of the Birch-Swinnerton-Dyer conjectures, this translates to interesting arithmetic information.

References [Enhancements On Off] (What's this?)

  • [1] Pierre Deligne, La conjecture de Weil. I, Inst. Hautes Études Sci. Publ. Math. 43 (1974), 273–307 (French). MR 0340258
  • [2] -, Valeurs de fonctions $ L$ et périodes d'intégrales, Proc. Sympos. Pure Math., vol. 33, part 2, Amer. Math. Soc., Providence, R.I., 1979, pp. 313-346.
  • [3] D. Goldfeld and C. Viola, Mean values of 𝐿-functions associated to elliptic, Fermat and other curves at the centre of the critical strip, J. Number Theory 11 (1979), no. 3 S. Chowla Anniversary Issue, 305–320. MR 544259, 10.1016/0022-314X(79)90004-0
  • [4] Goro Shimura, Introduction to the arithmetic theory of automorphic functions, Publications of the Mathematical Society of Japan, No. 11. Iwanami Shoten, Publishers, Tokyo; Princeton University Press, Princeton, N.J., 1971. Kan\cflex o Memorial Lectures, No. 1. MR 0314766
  • [5] John T. Tate, The arithmetic of elliptic curves, Invent. Math. 23 (1974), 179–206. MR 0419359
  • [6] André Weil, Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann. 168 (1967), 149–156 (German). MR 0207658

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 12A70, 10H10

Retrieve articles in all journals with MSC: 12A70, 10H10

Additional Information

Article copyright: © Copyright 1983 American Mathematical Society