Discrete mean square of the coefficients of symmetric square L-functions on certain sequence of positive numbers

被引：11

作者：

Sharma, Anubhav ^{[1
]}

Sankaranarayanan, Ayyadurai ^{[1
]}

机构：

[1] Univ Hyderabad Cent Univ, Sch Math & Stat, Prof CR Rao Rd, Hyderabad 500046, India

来源：

RESEARCH IN NUMBER THEORY | 2022年 / 8卷 / 01期

关键词：

Cauchy-Schwarz inequality; Symmetric square L-function; Holomorphic cusp forms; Principal Dirichlet character; FOURIER COEFFICIENTS; EULER PRODUCTS; CLASSIFICATION; ZEROS;

D O I：

10.1007/s40993-022-00319-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we will be concerned with the average behavior of the nth normalized Fourier coefficients of symmetric square L-function (i.e., L(s, sym(2)f)) over certain sequence of positive integers. Precisely, we prove an asymptotic formula for Sigma(a2+b2+c2+d2 <= x(a,b,c,d)is an element of Z4)lambda(2)(sym2f)(a(2) + b(2) +c(2) + d(2)), where x >= x(0) (sufficiently large), and L(s, sym(2)f) := Sigma(infinity)(n=1)lambda(sym2f)(n)/n(s).

引用

页数：13

共 20 条

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