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On Birch and Swinnerton-Dyer’s conjecture for elliptic curves with complex multiplication. I. (English) Zbl 0396.12011

MSC:
11R42 Zeta functions and \(L\)-functions of number fields
11R11 Quadratic extensions
11R37 Class field theory
14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
14K22 Complex multiplication and abelian varieties
14H52 Elliptic curves
14H45 Special algebraic curves and curves of low genus
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References:
[1] N. Arthaud : On Birch and Swinnerton-Dyer’s conjecture for elliptic curves with complex multiplication II (in preparation). · Zbl 0396.12011 · numdam:CM_1978__37_2_209_0 · eudml:89380
[2] J. Coates : p-Adic L-functions and Iwasawa’s theory (to appear in Proceedings of Durham symposium on algebraic number theory). · Zbl 0393.12027
[3] J. Coates , A. Wiles : Kummer’s criterion for Hurwitz numbers (to appear in Proceedings of International Conference on algebraic number theory, Kyoto, Japan, 1976). · Zbl 0369.12009
[4] J. Coates , A. Wiles : On the conjecture of Birch and Swinnerton-Dyer (to appear in Inventiones Mathematicae). · Zbl 0359.14009 · doi:10.1007/BF01402975 · eudml:142468
[5] S. Lang : Algebraic Number Theory , Addison-Wesley, 1970. · Zbl 0211.38404
[6] G. Robert : Unités elliptiques . Bull. Soc. Math. France, Mémoire 36, 1973. · Zbl 0314.12006 · numdam:MSMF_1973__36__5_0 · eudml:94657
[7] G. Shimura : Introduction to the arithmetic theory of automorphic functions . Pub. Math. Soc. Japan, 11, 1971. · Zbl 0221.10029
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