Partition into primes

理解黎曼ζ函数和其他l函数的矩是解析数论中的一个重要课题。在本专题中，学生将利用随机矩阵理论研究族中l -函数矩的联系。具体来说，研究的主题将是欧拉-哈达玛尔混合公式。其他课题包括研究l函数的零分布，如一级密度和对相关。在项目的最后部分，学生将专注于高属函数场上不同l函数族的混合公式的函数场类似物。

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.