LMFDB - Special value of an elliptic curve L-function (reviewed)

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The special value of an elliptic curve $E/\Q$ is the first nonzero value of $L^{(r)}(E,1)/r!$ for $r\in \Z_{\ge 0}$ , where $L(E,s)$ is the $L$ -function of $E$ in its arithmetic normalization.

The special value appears on the LHS of the formula in the Birch and Swinnerton-Dyer conjecture.

Authors:

Duc Khiem Huynh
Alina Bucur
David Farmer
Holly Swisher
Andrew Sutherland
John Jones

Knowl status:

Review status: reviewed
Last edited by Andrew Sutherland on 2024-10-26 17:34:07

Referred to by:

Not referenced anywhere at the moment.

History: (expand/hide all)

2024-10-26 17:34:07 by Andrew Sutherland (Reviewed)
2024-10-26 17:30:52 by Andrew Sutherland
2019-09-04 18:27:23 by David Farmer (Reviewed)
2018-06-19 15:38:28 by John Jones (Reviewed)

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Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.