Central values of additive twists of cuspidal L-functions-Reference-Cited by-同舟云学术

Central values of additive twists of cuspidal L-functions

Published:2021-04-02 Issue:0 Volume:0 Page:
ISSN:1435-5345
Container-title:Journal für die reine und angewandte Mathematik
language:en
Short-container-title:

Author:

Nordentoft Asbjørn Christian¹^ORCID

Affiliation:

1. Mathematical Institute , University of Bonn , Endenicher Allee 60 , Bonn 53115 , Germany

Abstract

Abstract Additive twists are important invariants associated to holomorphic cusp forms; they encode the Eichler–Shimura isomorphism and contain information about automorphic L-functions. In this paper we prove that central values of additive twists of the L-function associated to a holomorphic cusp form f of even weight k are asymptotically normally distributed. This generalizes (to k ≥ 4

{k\geq 4}

) a recent breakthrough of Petridis and Risager concerning the arithmetic distribution of modular symbols. Furthermore, we give as an application an asymptotic formula for the averages of certain “wide” families of automorphic L-functions consisting of central values of the form L ⁢ ( f ⊗ χ , 1 / 2 )

{L(f\otimes\chi,1/2)}

with χ a Dirichlet character.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

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