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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
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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] P. Deligne, La conjecture de Weil. I, Inst. Hautes Études Sci. Publ. Math. 43 (1973), 273-307. MR 0340258 (49:5013)
  • [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), 305-320. MR 544259 (80j:10046)
  • [4] G. Shimura, Introduction to the arithmetic theory of automorphic functions, Princeton Univ. Press, Princeton, N.J., 1971. MR 0314766 (47:3318)
  • [5] J. Tate, The arithmetic of elliptic curves, Invent. Math. 23 (1974), 179-206. MR 0419359 (54:7380)
  • [6] A. Weil, Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann. 168 (1967), 149-156. MR 0207658 (34:7473)

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Article copyright: © Copyright 1983 American Mathematical Society

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