Topics in Multiplicative Number Theory

该项目将在函数域的背景下研究算术函数的平均值的几个问题。具体地说，它将集中在使用基廷和鲁德尼克开发的新技术的短间隔和算术级数中的算术函数的平均值。该项目的另一个方面是研究函数域上L函数的平均值，重点研究零点的分布及其统计。

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.