Mean square of zeta function, circle problem and divisor problem revisited

TL;DR

This paper revisits the mean square of the zeta function, the circle problem, and the divisor problem, providing refined results and methods building upon previous work by the authors.

Contribution

It introduces a simple variant of earlier methods that improves key theorems related to the mean square of the zeta function and classical number theory problems.

Findings

Enhanced bounds for the mean square of the zeta function

Refined estimates for the circle problem

Improved divisor problem results

Abstract

This paper is closely related to the recent work [BW17] of the same authors and our purpose is to elaborate more on some of the results and methods from [BW17]. More specifically our goal is two-fold. Firstly, we will indicate how a simple variant related to Section 4 in [BW17] leads to the following improvements of Theorem 3 in [BW17]