素数分布是数论研究中的核心课题之一，二次曲面上的素点分布是素数分布理论的深化，具有重要的理论意义。近年来，关于二次型为对角型所表示二次曲面上的素点分布的研究处于瓶颈期，探索新的研究方法和研究思想正逐步成为该研究方向发展的当务之急。本项目拟采用新的研究工具Kloosterman圆法，并结合Harman筛法和向量筛法开展该方向的研究。关于二次型为非对角型所表示二次曲面上的素点分布的研究，目前只有一些初步的结果，本项目拟采用Dirichlet多项式的均值估计以及自守L-函数傅立叶系数的均值估计等均值估计法开展该方向的研究。本项目计划将新研究工具Kloosterman圆法、Harman筛法、向量筛法、自守L-函数的零点分布理论与素数分布理论相结合，实质性地推进二次曲面上的素点分布的研究。

The distribution of prime points on quadric surface deepens the distribution of primes, which is one of the core topics in number theory. The study of this topic has important theoretical significance. In recent years, the study of the distribution of prime points on quadric surface represented by diagonal quadratic forms is stepping into a bottleneck period. Therefore, exploring new research methods and research ideas is a top priority for the development of this field. We are going to use a new instrument, Kloosterman circle method, combining Harman sieve and the vector sieve to study this field. There are only some preliminary results in the study of the distribution of prime points on quadric surface represented by nondiagonal quadratic forms. We are going to use the method of mean values to study this field, such as the mean value estimates of Dirichlet polynomials, the mean value estimates of the Fourier coefficients of automorphic L-function, etc. This project will promote the research of the distribution of prime points on quadric surface by combining Kloosterman circle method, Harman sieve, the vector sieve, zero density of automorphic L-functions and the distribution of primes.