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This is a Quantitative Study study.

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October 23, 2025

Higher power sums of Fourier coefficients of symmetric square L-functions

Key Points

Improved error estimates were found in sums of Fourier coefficients from symmetric square L-functions, emphasizing their significance.
Specifically, the sums evaluated involve the normalized primitive holomorphic Hecke eigenforms across certain limits.
Assessment involved using advanced techniques related to modular forms and symmetric square L-functions.
Findings may enhance understanding of the distribution of Fourier coefficients in number theory.

Abstract

Abstract Let f (z) be the normalized primitive holomorphic Hecke eigenforms of even integral weight k for the full modular group SL (2, Z) and denote L (s, sym^2f) be the symmetric square L -function attached to f (z). Suppose that ₒₘ₌^₂f (n) be the Fourier coefficient of L (s, sym^2f). In this paper, we investigate the sum ₍ ₗ ^jₒₘ₌^₂f (n) for j 3 and obtain some new results which improve on previous error estimates. We also consider the sum ₍ ₗ^j₅ (n^2) and get some similar results.

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Cite This Study

Jinzhi Feng (Tue,) studied this question.

synapsesocial.com/papers/68fa1210f9f8b44535bfcecb https://doi.org/https://doi.org/10.1017/s0013091525101028

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