Shifted convolution sum with weighted average : $GL(3) \times GL(3)$ setup

TL;DR

This paper establishes non-trivial bounds for weighted average shifted convolution sums in the $GL(3) imes GL(3)$ setting using the circle method, advancing understanding in automorphic forms and analytic number theory.

Contribution

It introduces novel estimates for weighted averages of $GL(3) imes GL(3)$ shifted convolution sums employing the circle method, a new approach in this context.

Findings

Proves non-trivial bounds for weighted shifted convolution sums.

Develops circle method techniques for $GL(3) imes GL(3)$ sums.

Enhances analytic tools for automorphic form analysis.

Abstract

This article will prove non-trivial estimates for the average and weighted average version of general $GL(3) \times GL(3)$ shifted convolution sums by using the circle method.