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Pot-pourri elliptique (complexe et) p-adique illustré. (French) Zbl 0577.14015
Théorie des nombres, Sémin. Delange-Pisot-Poitou, Paris 1983-84, Prog. Math. 59, 105-113 (1985).
[For the entire collection see Zbl 0561.00004.]
In this note the author illustrates the conjecture (B) of her joint paper with D. Bernardi and N. Stephens [J. Reine Angew. Math. 351, 129-170 (1984; Zbl 0529.14018)] by two numerical examples and relates it to the the main conjecture of Birch and Swinnerton-Dyer, and a result of B. Perrin-Riou [Invent. Math. 70, 369-398 (1983; Zbl 0547.14025)]. The conjecture relates the vanishing order and the leading coefficient at \(s=1\) of the p-adic L-function of an elliptic curve over \({\mathbb{Q}}\) to the corresponding values of its Hasse-Weil L-function.
Reviewer: F.Herrlich

14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
14H25 Arithmetic ground fields for curves
14G20 Local ground fields in algebraic geometry
14H52 Elliptic curves