Linnik算术级数素数估计的拟态证明
数论
2024-09-18 v6
摘要
在本文中，我们采用拟态方法，证明了von Mangoldt函数在算术级数上求和的强一致估计。该估计类似于Linnik在其试图证明关于算术级数中最小素数大小的著名定理时所建立的估计。我们的工作建立在Granville、Harper与Soundararajan的拟态大筛法思想之上，并借鉴了Koukoulopoulos关于小均值乘性函数处理的见解。
引用
@article{arxiv.2209.14538,
title = {A pretentious proof of Linnik's estimate for primes in arithmetic progressions},
author = {Stelios Sachpazis},
journal= {arXiv preprint arXiv:2209.14538},
year = {2024}
}
备注
22 pages; A small necessary fix in the proof of Theorem 1.1 was applied, minor text changes in the Abstract and the Introduction were made, Lemma 2.1 and Theorem 2.4 were added and the proof of Lemma 2.5 (previously Lemma 2.3) was rewritten. A reference and a remark (Remark 1.1) were added and another reference was updated