Computation of central value of quadratic twists of modular L-functions
Number Theory
2021-07-14 v1
Abstract
Let f be a newform of weight two, prime level p. If D is a fundamental discriminant, define the twisted L-function L(f,D,s) to be the L-function associated to the twist of f by the quadratic character of conductor D. In this paper we consider the question of computing the family of twisted central values {L(f,D,1) : |D| <= x} for some x, by using an explicit version of Waldspurger's formula relating the central values L(f,D,1) to the |D|-th Fourier coefficient of weigth 3/2 modular forms in Shimura correspondence with f.
Keywords
Cite
@article{arxiv.math/0606762,
title = {Computation of central value of quadratic twists of modular L-functions},
author = {Zhengyu Mao and Fernando Rodriguez-Villegas and Gonzalo Tornaría},
journal= {arXiv preprint arXiv:math/0606762},
year = {2021}
}
Comments
13 pages; to appear in "Ranks of elliptic curves and random matrix theory." (2005)