On the second moment of the Fourier coefficients of symmetric power L-function over two sparse sequences of positive integers

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发表日期：

2025年7月22日

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Jinzhi Feng

摘要

Let f(z) be the normalized primitive holomorphic Hecke eigenforms of even integral weight k for the full modular group $SL(2,\mathbb {Z})$ $S L (2, Z)$ . In this paper, we investigate the second moment of Fourier coefficients of symmetric power L-function $L(s,\textrm{sym}^{j}f )$ $L (s, {sym}^{j} f)$ over two sparse sequences of positive integers and improve on previous error estimates.