The Average Behaviors of the Fourier Coefficients of j-th Symmetric Power L-Function over Two Sparse Sequences of Positive Integers

IF 0.7 4区 数学 Q2 MATHEMATICS
Huafeng Liu, Xiaojie Yang
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引用次数: 0

Abstract

Suppose that x is a sufficiently large number and \(j\ge 2\) is any integer. Let \(L(s, \textrm{sym}^j f)\) be the j-th symmetric power L-function associated with the primitive holomorphic cusp form f of weight k for the full modular group SL\(_{2}(\mathbb {Z})\). Also, let \(\lambda _{\textrm{sym}^j f}(n)\) be the n-th normalized Dirichlet coefficient of \(L(s, \textrm{sym}^j f)\). In this paper, we establish asymptotic formulas for sums of Dirichlet coefficients \(\lambda _{\textrm{sym}^j f}(n)\) over two sparse sequences of positive integers, which improves previous results.

两个正整数稀疏序列上 j-th 对称幂 L 函数傅里叶系数的平均行为
假设 x 是一个足够大的数,并且 \(j\ge 2\) 是任意整数。让(L(s, textrm{sym}^j f))是与全模态群 SL\(_{2}(\mathbb {Z})\)的权重为 k 的原始全纯尖顶形式 f 相关的第 j 次对称幂 L 函数。同时,设 \(\lambda _{\textrm{sym}^j f}(n)\) 是 \(L(s, \textrm{sym}^j f)\) 的第 n 个归一化的 Dirichlet 系数。本文建立了两个正整数稀疏序列上的 Dirichlet 系数总和 \(\lambda _{textrm{sym}^j f}(n)\) 的渐近公式,改进了之前的结果。
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来源期刊
Bulletin of The Iranian Mathematical Society
Bulletin of The Iranian Mathematical Society Mathematics-General Mathematics
CiteScore
1.40
自引率
0.00%
发文量
64
期刊介绍: The Bulletin of the Iranian Mathematical Society (BIMS) publishes original research papers as well as survey articles on a variety of hot topics from distinguished mathematicians. Research papers presented comprise of innovative contributions while expository survey articles feature important results that appeal to a broad audience. Articles are expected to address active research topics and are required to cite existing (including recent) relevant literature appropriately. Papers are critically reviewed on the basis of quality in its exposition, brevity, potential applications, motivation, value and originality of the results. The BIMS takes a high standard policy against any type plagiarism. The editorial board is devoted to solicit expert referees for a fast and unbiased review process.
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