Shifted convolution and the Titchmarsh divisor problem over F_q[t]

TL;DR

This paper addresses a function field analogue of classical analytic number theory problems, focusing on auto-correlations of divisor functions over large finite fields, providing new insights into their behavior.

Contribution

It introduces a novel approach to the Titchmarsh divisor problem in the setting of function fields over finite fields, extending classical results.

Findings

Established asymptotic formulas for divisor function auto-correlations

Demonstrated the behavior of divisor functions in large finite fields

Connected classical number theory problems to function field analogues

Abstract

In this paper we solve a function field analogue of classical problems in analytic number theory, concerning the auto-correlations of divisor functions, in the limit of a large finite field.