What question did this study set out to answer?

This work aims to analyze the shifted convolution sum of coefficients from the symmetric square L-function.

May 8, 2026

Shifted convolution sum for the coefficients of symmetric square L -function

Key Points

This work aims to analyze the shifted convolution sum of coefficients from the symmetric square L-function.
Investigated the shifted convolution sum for coefficients of symmetric square L-functions.
Focused on the range where the parameters fulfill H > N^{1/4}.
Established a non-trivial bound for the shifted convolution sum.
Demonstrated significant behavior for the coefficients of the symmetric square L-function under the specified conditions.

Abstract

Let f be a normalized primitive holomorphic cusp form of even integral weight for the full modular group =SL (2, Z). Denote by ₒₘ₌^₂f (n) the n th normalized coefficient of the Dirichlet series expansion of the symmetric square L -function L (s, sym^2f). In this paper, we are interested in the shifted convolution sum equation*₇ ₇₍ ₍ ₂₍ₒₘ₌^₂f (n) ₒₘ₌^₂f (n+h). equation* We establish a non-trivial bound for H N^1/4.

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