论文标题
Bombieri-Vinogradov定理用于nilSequens
The Bombieri-Vinogradov theorem for nilsequences
论文作者
论文摘要
我们为Von Mangoldt功能的Bombieri-Vinogradov类型建立了$λ（n）$ twist的结果。特别是，我们获得了von Mangoldt函数的Bombieri-Vinogradov类型结果，该功能由任何多项式期$ e（p（n））$扭曲；在线性指数曲折的情况下，获得的结果与先前已知的结果一样强。我们得出了这些结果的许多应用。首先，我们表明Primes $ p $遵守“ nil-bohr set”条件，例如$ \ | |αp^k \ | <\ varepsilon $，表现出界限。其次，我们表明陈素在尼尔·波尔集合中分布良好，从而推广了matomäki的结果。第三，我们将几乎所有$ q $的算术进展属于算术级别的素数上的线性方程式上的绿色 - 塔概括为算术的素数。
We establish results of Bombieri-Vinogradov type for the von Mangoldt function $Λ(n)$ twisted by a nilsequence. In particular, we obtain Bombieri-Vinogradov type results for the von Mangoldt function twisted by any polynomial phase $e(P(n))$; the results obtained are as strong as the ones previously known in the case of linear exponential twists. We derive a number of applications of these results. Firstly, we show that the primes $p$ obeying a "nil-Bohr set" condition, such as $\|αp^k\|<\varepsilon$, exhibit bounded gaps. Secondly, we show that the Chen primes are well-distributed in nil-Bohr sets, generalizing a result of Matomäki. Thirdly, we generalize the Green-Tao result on linear equations in the primes to primes belonging to an arithmetic progression to large modulus $q\leq x^θ$, for almost all $q$.
