论文标题
Linnik对算术进展中素数的估计的自命不凡的证明
A pretentious proof of Linnik's estimate for primes in arithmetic progressions
论文作者
论文摘要
在本文中，我们采用了自命不凡的方法，并证明了von Mangoldt函数$λ$在算术进程中的总和。这种估计与林尼克（Linnik）在试图证明他著名的定理有关算术进展最小的质量数量的估计中建立的估计值类似。我们的作品是基于来自Granville，Harper和Soundararajan的自命不凡的大筛子的想法，并且还借鉴了Koukoulopoulos对具有较小平均值的乘法功能的治疗。
In the present paper, we adopt a pretentious approach and prove a strongly uniform estimate for the sums of the von Mangoldt function $Λ$ on arithmetic progressions. This estimate is analogous to 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.
