Publications Mathématiques de Besançon
Algèbre et Théorie des Nombres
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 Home 1975-2014 archives All online articles Advanced Search Latest articles Search for an article Table of contents for this volume | Previous article Christian WuthrichThe sub-leading coefficient of the $L$-function of an elliptic curvePublications mathématiques de Besançon (2016), p. 95-96 Article PDF Class. Math.: 11G40Keywords: $L$-functions of elliptic curves, Birch-Swinnerton-Dyer conjecture AbstractWe show that there is a relation between the leading term at $s=1$ of an $L$-function of an elliptic curve defined over an number field and the term that follows. Bibliography[1] Christophe Breuil, Brian Conrad, Fred Diamond & Richard Taylor, “On the modularity of elliptic curves over $\mathbf{Q}$: wild 3-adic exercises”, J. Amer. Math. Soc. 14 (2001) no. 4, p. 843-939  MR 1839918 |  Zbl 0982.11033[2] Pierre Colmez, “Périodes des variétés abéliennes à multiplication complexe”, Ann. of Math. (2) 138 (1993) no. 3, p. 625-683  MR 1247996 |  Zbl 0826.14028[3] Dale Husemöller, Elliptic curves, Graduate Texts in Mathematics 111, Springer-Verlag, New York, 2004, With appendices by Otto Forster, Ruth Lawrence and Stefan Theisen  MR 2024529 |  Zbl 0605.14032