Frontiers of Mathematics in China >

2020 , Vol. 15 >Issue 1: 205 - 213

DOI: https://doi.org/10.1007/s11464-020-0817-1

RESEARCH ARTICLE

Mean-square estimate of automorphic L-functions

  • Weili YAO
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  • Department of Mathematics, Shanghai University, Shanghai 200444, China

Received date: 17 May 2019

Accepted date: 19 Jan 2020

Published date: 15 Feb 2020

Copyright

2020 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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Abstract

Let f be a holomorphic Hecke cusp form with even integral weight k≥2 for the full modular group, and let χ be a primitive Dirichlet character modulo q. Let Lf(s,χ) be the automorphic L-function attached to f and χ. We study the mean-square estimate of Lf(s,χ) and establish an asymptotic formula.

Key words： Automorphic L-function; cusp form; Fourier coe_cient

Cite this article

Weili YAO . Mean-square estimate of automorphic L-functions[J]. Frontiers of Mathematics in China, 2020 , 15(1) : 205 -213 . DOI: 10.1007/s11464-020-0817-1

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