The generalized Montgomery-Hooley formula: A survey
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914579145031680 |
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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 |