Experimental Mathematics

Critical Values of Derivatives of Twisted Elliptic $L$-Functions

Jack Fearnley and Hershy Kisilevsky

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Abstract

Let $L(E/\Q,s)$ be the $L$-function of an elliptic curve $E$ defined over the rational field $\Q$. We examine special values of the derivatives $L^{\prime}(E,1,\chi)$ of twists by Dirichlet characters of $L(E/\Q,s)$ when $L(E,1,\chi)=0$.

Article information

Source
Experiment. Math., Volume 19, Issue 2 (2010), 149-160.

Dates
First available in Project Euclid: 17 June 2010

Permanent link to this document
https://projecteuclid.org/euclid.em/1276784786

Mathematical Reviews number (MathSciNet)
MR2676744

Zentralblatt MATH identifier
1221.11148

Subjects
Primary: 11G05: Elliptic curves over global fields [See also 14H52] 11G40: $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture [See also 14G10] 11Y40: Algebraic number theory computations

Keywords
Elliptic curves $L$-functions

Citation

Fearnley, Jack; Kisilevsky, Hershy. Critical Values of Derivatives of Twisted Elliptic $L$-Functions. Experiment. Math. 19 (2010), no. 2, 149--160. https://projecteuclid.org/euclid.em/1276784786


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