Mean square of zeta function, circle problem and divisor problem revisited
Analysis of PDEs
2023-07-18 v2 Number Theory
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]
Keywords
Cite
@article{arxiv.1709.04340,
title = {Mean square of zeta function, circle problem and divisor problem revisited},
author = {Jean Bourgain and Nigel Watt},
journal= {arXiv preprint arXiv:1709.04340},
year = {2023}
}
Comments
A problem with the proofs of Propositions 2 and 3 (a gap or fault in the reasoning used to claim that the expression in (3.9) is dominated by that in (3.11)); a similar problem with the proof of Proposition $1'$ (it is hard to justify the particular application of the Bourgain-Guth reduction theory implicit in a paragraph above Proposition $1'$). Theorems 1, 2 and 3 lose their status as theorems