The sub-leading coefficient of the L-function of an elliptic curve
Publications Mathématiques de Besançon (2016), pp. 95-96.

On montre une relation entre le terme dominant de la série L en s=1 d’une courbe elliptique définie sur un corps de nombre et le terme suivant.

We 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.

Reçu le : 2016-01-17
Publié le : 2016-12-13
DOI : https://doi.org/10.5802/pmb.o-8
Classification : 11G40
Mots clés: L-functions of elliptic curves, Birch-Swinnerton-Dyer conjecture
@article{PMB_2016____95_0,
     author = {Christian Wuthrich},
     title = {The sub-leading coefficient of the $L$-function of an elliptic curve},
     journal = {Publications Math\'ematiques de Besan\c con},
     pages = {95--96},
     publisher = {Presses universitaires de Franche-Comt\'e},
     year = {2016},
     doi = {10.5802/pmb.o-8},
     zbl = {1367.11057},
     language = {en},
     url = {pmb.centre-mersenne.org/item/PMB_2016____95_0/}
}
Christian Wuthrich. The sub-leading coefficient of the $L$-function of an elliptic curve. Publications Mathématiques de Besançon (2016), pp. 95-96. doi : 10.5802/pmb.o-8. https://pmb.centre-mersenne.org/item/PMB_2016____95_0/

[1] Christophe Breuil; Brian Conrad; Fred Diamond; Richard Taylor On the modularity of elliptic curves over Q: wild 3-adic exercises, J. Amer. Math. Soc., Volume 14 (2001) no. 4, pp. 843-939 | Article | MR 1839918 | Zbl 0982.11033

[2] Pierre Colmez Périodes des variétés abéliennes à multiplication complexe, Ann. of Math. (2), Volume 138 (1993) no. 3, pp. 625-683 | Article | Zbl 0826.14028

[3] Dale Husemöller Elliptic curves, Graduate Texts in Mathematics, Volume 111, Springer-Verlag, New York, 2004, xxii+487 pages (With appendices by Otto Forster, Ruth Lawrence and Stefan Theisen) | MR 2024529 | Zbl 1040.11043