Three Lectures on the Riemann Zeta-Function

TL;DR

This paper provides an accessible overview of the Riemann zeta function, covering its zeros, the prime number theorem, the Riemann hypothesis, and connections to random matrix theory.

Contribution

It offers a comprehensive exposition on key topics related to the Riemann zeta function, integrating classical results with modern conjectures and models.

Findings

Explanation of the distribution of zeros of the zeta function

Discussion of the prime number theorem and its implications

Introduction to random matrix models related to zeta zeros

Abstract

These expository lectures focus on the distribution of zeros of the Riemann zeta function. The topics include the prime number theorem, the Riemann hypothesis, mean value theorems, and random matrix models.