素数分布是解析数论研究的核心内容之一. 张益唐关于孪生素数的突破性进展和 Sarnak 等数学家提出的关于素数分布的猜想为这一课题的研究注入了新的活力. 在该项目中, 申请人拟研究以下两部分内容: 1. 关于小区间上的素变数指数和的Bombieri-Vinogradov 型定理及其应用; 2. 关于 Beatty 数和 Pyateckii-Šapiro 数的素变数指数和的 Bombieri-Vinogradov 型定理及其应用.

Distribution of primes is one of the central topics in analytic number theory. The breakthrough of Zhang Yitang on twin primes and Sarnak's Conjecture on primes obits provide some new ideas and methods for the study of distribution of primes. In this project, we will research on the following problems: 1. Theorems of Bombieri-Vinogradov type for exponential sums over primes in short intervals and applications; 2. Theorems of Bombieri-Vinogradov type for exponential sums over Beatty and Pyateckii-Šapiro primes and applications.