Note on Triple correlations of Fourier coefficients of cusp forms

TL;DR

This paper presents a simplified approach to analyzing unbalanced shifted convolution sums of Fourier coefficients of cusp forms, improving upon earlier results achieved through more complex methods.

Contribution

It introduces a straightforward method for studying shifted convolution sums, enhancing the efficiency and clarity over previous advanced techniques.

Findings

Improved bounds on shifted convolution sums

Simplified proof technique

Enhanced understanding of Fourier coefficient correlations

Abstract

In this short note, we treat an unbalanced shifted convolution sum of Fourier coefficients of cusp forms by a rather simple argument. Our result improves previous results established by more advanced approaches.