Mean-square estimate of automorphic <i>L</i>-functions

doi:10.1007/s11464-020-0817-1

Front. Math. China

2020, Vol. 15

Issue (1) : 205-213 https://doi.org/10.1007/s11464-020-0817-1

RESEARCH ARTICLE

Mean-square estimate of automorphic L-functions

Weili YAO(

)

Department of Mathematics, Shanghai University, Shanghai 200444, China

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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 $L f (s, χ)$ be the automorphic L-function attached to f and $χ$ . We study the mean-square estimate of $L f (s, χ)$ and establish an asymptotic formula.

Keywords Automorphic L-function cusp form Fourier coe_cient

Corresponding Author(s): Weili YAO

Issue Date: 09 March 2020

Cite this article:

Weili YAO. Mean-square estimate of automorphic L-functions[J]. Front. Math. China, 2020, 15(1): 205-213.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-020-0817-1
https://academic.hep.com.cn/fmc/EN/Y2020/V15/I1/205

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