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Central values of additive twists of cuspidal L-functions

  • Asbjørn Christian Nordentoft ORCID logo EMAIL logo
Published/Copyright: April 2, 2021

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 k4) 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(fχ,1/2) with χ a Dirichlet character.

Acknowledgements

I would like to express my gratitude to my advisor Morten Risager for suggesting this problem to me and for our countless stimulating discussions. I would also like to thank Yiannis Petridis for his time and insight.

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Received: 2020-05-04
Revised: 2021-02-25
Published Online: 2021-04-02
Published in Print: 2021-07-01

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