The generalized Montgomery-Hooley formula: A survey

Fuente: arXiv
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Main Author: Vaughan, Robert C.
Format: Preprint
Published: 2026
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author Vaughan, Robert C.
author_facet Vaughan, Robert C.
contents This memoir is a survey of theorems and inequalities which have grown out of, and extended, the seminal estimate of Montgomery \cite{HM70} \begin{multline*} V(x,Q)=\sum_{q\le Q}\sum_{\substack{a=1\\ (a,q)=1}}^q \left| ψ(x;q,a) - \frac{x}{ϕ(q)} \right|^2 \\ = Qx\log x + \textstyle O\big(Qx\log\frac{2x}{Q}\big) + O\big(x^2(\log x)^{-A}\big)., \end{multline*}
format Preprint
id arxiv_https___arxiv_org_abs_2605_18996
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle The generalized Montgomery-Hooley formula: A survey
Vaughan, Robert C.
Number Theory
11N25
This memoir is a survey of theorems and inequalities which have grown out of, and extended, the seminal estimate of Montgomery \cite{HM70} \begin{multline*} V(x,Q)=\sum_{q\le Q}\sum_{\substack{a=1\\ (a,q)=1}}^q \left| ψ(x;q,a) - \frac{x}{ϕ(q)} \right|^2 \\ = Qx\log x + \textstyle O\big(Qx\log\frac{2x}{Q}\big) + O\big(x^2(\log x)^{-A}\big)., \end{multline*}
title The generalized Montgomery-Hooley formula: A survey
topic Number Theory
11N25
url https://arxiv.org/abs/2605.18996