稀疏集合中整数处 L 函数乘积的傅立叶系数振荡

IF 0.5 3区数学 Q3 MATHEMATICS

International Journal of Number Theory Pub Date : 2024-04-10 DOI:10.1142/s1793042124500854

Babita, Mohit Tripathi, Lalit Vaishya

引用次数: 0

摘要

设 f 是全模态群 SL2(ℤ) 权重为 k 的归一化赫克特征形式。在本文中，我们得到了与 Rankin-Selberg L 函数 R(s,f×f) 的傅里叶系数相关的一般除数函数的高阶矩的渐近值，R(s,f×f) 在整数处由固定判别式 D<0 的原始积分正定二元二次方程形式（还原形式）表示。当还原形式为𝒬(x1,x2)=x12+x22 时，我们改进了以前的结果。

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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Oscillations of Fourier coefficients of product of L-functions at integers in a sparse set

Let $f$ be a normalized Hecke eigenform of weight $k$ for the full modular group $S L_{2} (ℤ)$ . In this paper, we obtain the asymptotic of higher moments of general divisor functions associated to the Fourier coefficients of Rankin–Selberg $L$ -functions $R (s, f \times f)$ , supported at the integers represented by primitive integral positive-definite binary quadratic forms (reduced forms) of a fixed discriminant $D < 0 .$ We improve previous results in the case when the reduced form is given by $𝒬 (x_{1}, x_{2}) = x_{1}^{2} + x_{2}^{2} .$

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来源期刊

International Journal of Number Theory 数学-数学

CiteScore

1.10

自引率

14.30%

发文量

审稿时长

4-8 weeks

期刊介绍： This journal publishes original research papers and review articles on all areas of Number Theory, including elementary number theory, analytic number theory, algebraic number theory, arithmetic algebraic geometry, geometry of numbers, diophantine equations, diophantine approximation, transcendental number theory, probabilistic number theory, modular forms, multiplicative number theory, additive number theory, partitions, and computational number theory.