素数分布及相关问题研究

本项目主要研究素数分布问题，包括华林-哥德巴赫问题,一般丢翻图方程的素数解问题以及小密度集合上的的素数分布问题。 将重点研究华林-哥德巴赫问题中的几乎相等问题及例外集问题。具体方法包括圆法、筛法的应用，素变数指数和的估计以及指数和的均值估计。此外，还将研究GLn(Z)上自守L-函数的零点密度估计和在素数分布问题上的应用。

In this project, we will research on problems concerning distribution of primes, including the Waring-Goldbach problems and the prime solutions of general Diophantine equations and prime distribution in thin subset. We will focus on the Waring-Goldbach problem of almost equal prime variables and the exceptional set estimates. Our methods include the circle method, sieve method, exponential sums over primes and mean-value estimates. We will also study zero-density estimates for automorphic L-functions on GLn and consider applications in problems concerning distribution of primes.