对算术数列中素数的林尼克估计的自命不凡的证明

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematika Pub Date : 2023-06-09 DOI:10.1112/mtk.12211

Stelios Sachpazis

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引用次数: 0

摘要

在本文中，作者采用一种自命的方法，恢复了Linnik对算术数列上的von Mangoldt函数Λ的和的估计。它是林尼克在试图证明他著名的关于等差数列最小素数大小的定理时建立的一个估计的类似物。我们的工作建立在Granville, Harper和Soundararajan的自命不凡的大筛选的思想之上，它也借鉴了Koukoulopoulos对小平均值乘法函数的处理的见解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A pretentious proof of Linnik's estimate for primes in arithmetic progressions

In the present paper, the author adopts a pretentious approach and recovers an estimate obtained by Linnik for the sums of the von Mangoldt function Λ on arithmetic progressions. It is the analogue of an estimate that Linnik established in his attempt to prove his celebrated theorem concerning the size of the smallest prime number of an arithmetic progression. Our work builds on ideas coming from the pretentious large sieve of Granville, Harper, and Soundararajan and it also borrows insights from the treatment of Koukoulopoulos on multiplicative functions with small averages.

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来源期刊

Mathematika MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.