Partition into primes

了解黎曼Zeta函数和其他L函数的矩是解析数论中的一个重要课题。在这个项目中，学生将用随机矩阵理论研究L函数在族中的矩的联系。具体地说，主要研究对象将是欧拉-阿达玛混合公式。其他主题包括研究L函数的零点分布，如一级密度和对相关。在项目的最后部分，学生将专注于L不同家族的混合公式的函数域类比--更高亏格函数域上的函数。

It is an important topic in analytic number theory to understand the moments of the Riemann zeta-function and other L-functions. In this project the student will study the connections involving moments of L-functions in families with random matrix theory. Specifically, the main subject of study will be the Euler-Hadamard hybrid formula. Other topics include the study of distribution of zeros of L-functions such as one-level density and pair correlation. For the final parts of the project the student will focus on function field analogues of the Hybrid formula for different families of L-functions over function fields of higher genus.