Computation of central value of quadratic twists of modular L-functions

Details Computation of central value of quadratic twists of modular L-functions Computation of central value of quadratic twists of modular L-functions

2006-06-29

arxiv.org/abs/math/0606762v1

Mathematics

Number Theory

13 pages; to appear in "Ranks of elliptic curves and random matrix theory." (2005)

Scientific paper

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.

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