Function fields and random matrices

TL;DR

This survey explores the connection between families of L-functions over function fields and the distribution of matrices in classical groups, illustrating key examples without detailed proofs.

Contribution

It provides an informal overview of how matrices from classical groups relate to L-functions in function fields, highlighting key examples and insights.

Findings

Illustrates the distribution of matrices in classical groups from L-function families

Provides insights into the connection between function fields and random matrix theory

Highlights key examples without formal proofs

Abstract

This is a survey article written for a workshop on L-functions and random matrix theory at the Newton Institute in July, 2004. The goal is to give some insight into how well-distributed sets of matrices in classical groups arise from families of $L$-functions in the context of function fields of curves over finite fields. The exposition is informal and no proofs are given; rather, our aim is to illustrate what is true by considering key examples.