Shifted convolution of divisor function $d_3$ and Ramanujan $\tau$ function

TL;DR

This paper investigates the shifted convolution sum involving the divisor function d_3 and the Ramanujan tau function, aiming to understand their combined behavior and interactions.

Contribution

It provides new insights into the shifted convolution sums of d_3 and tau, a topic not extensively explored before.

Findings

Derived bounds for the shifted convolution sum

Established connections between divisor functions and tau

Enhanced understanding of their joint distribution

Abstract

We study the shifted convolution sum of the divisor function $d_3$ and the Ramanujan $\tau$ function.