Asymptotics for the second moment of the Dirichlet coefficients of symmetric power L-functions

IF 0.5 4区数学 Q3 MATHEMATICS

Lithuanian Mathematical Journal Pub Date : 2024-06-24 DOI:10.1007/s10986-024-09636-0

Xue Han, Huafeng Liu

引用次数: 0

Abstract

Let m ≥ 2 be an integer. Let f be a holomorphic Hecke eigenform of even weight k for the full modular group SL(2, ℤ). Denote by λ_Sym^m _f (n) the nth normalized Dirichlet coefficient of the corresponding symmetric power L-function L(s, Sym^m f) related to f. In this paper, we study the average behavior of the second moment of the Dirichlet coefficients λ_Sym^m _f (n) and establish its asymptotic formula.

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对称幂 L 函数 Dirichlet 系数第二矩的渐近线

设 m ≥ 2 为整数。设 f 是全模态群 SL(2, ℤ) 偶数权 k 的全形赫克特征形式。用 λSymm f (n) 表示与 f 有关的相应对称幂 L 函数 L(s, Symm f) 的第 n 个归一化 Dirichlet 系数。本文将研究 Dirichlet 系数 λSymm f (n) 的第二矩的平均行为，并建立其渐近公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Lithuanian Mathematical Journal 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Lithuanian Mathematical Journal publishes high-quality original papers mainly in pure mathematics. This multidisciplinary quarterly provides mathematicians and researchers in other areas of science with a peer-reviewed forum for the exchange of vital ideas in the field of mathematics. The scope of the journal includes but is not limited to: Probability theory and statistics; Differential equations (theory and numerical methods); Number theory; Financial and actuarial mathematics, econometrics.