Topics in Multiplicative Number Theory

本课题将探讨函数域背景下算术函数均值的几个问题。具体地说，它将集中在算术函数的均值在短间隔和在等差数列使用基廷和鲁德尼克开发的新技术。该项目的另一个方面是研究函数域上l函数的平均值，重点研究零的分布及其统计。

The project will investigate several problems about mean values of arithmetic functions in the context of function fields. Specifically, it will focus on the mean value of arithmetic functions in short intervals and in arithmetic progressions using the new techniques developed by Keating and Rudnick. Another aspect of the project is the study of mean values of L-functions over function fields focusing on the study of the distribution of zeros and their statistics.