Experimental Mathematics

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

Jack Fearnley and Hershy Kisilevsky

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Abstract

Let $L (E /\mathbb{Q} , s)$ be the $L$-function of an elliptic curve $E$ defined over the rational field $\mathbb{Q}$. Assuming the Birch–Swinnerton-Dyer conjectures, we examine special values of the $r$th derivatives, $L^{(r)}(E , 1, \chi)$, of twists by Dirichlet characters of $L (E /\mathbb{Q} , s)$ when $L (E , 1, \chi) = • • • = L^{(r−1)} (E , 1, \chi) = 0$.

Article information

Source
Experiment. Math., Volume 21, Issue 3 (2012), 213-222.

Dates
First available in Project Euclid: 13 September 2012

Permanent link to this document
https://projecteuclid.org/euclid.em/1347541272

Mathematical Reviews number (MathSciNet)
MR2988574

Zentralblatt MATH identifier
1302.11040

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 Higher Derivatives of Twisted Elliptic $L$-Functions. Experiment. Math. 21 (2012), no. 3, 213--222. https://projecteuclid.org/euclid.em/1347541272


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