Introduction

Summary

The theory of automorphic forms and L-functions for the group of n × n invertible real matrices (denoted GL(n, ℝ)) with n ≥ 3 is a relatively new subject. The current literature is rife with 150+ page papers requiring knowledge of a large breadth of modern mathematics making it difficult for a novice to begin working in the subject. The main aim of this book is to provide an essentially self-contained introduction to the subject that can be read by someone with a mathematical background consisting only of classical analysis, complex variable theory, and basic algebra – groups, rings, fields. Preparation in selected topics from advanced linear algebra (such as wedge products) and from the theory of differential forms would be helpful, but is not strictly necessary for a successful reading of the text. Any Lie or representation theory required is developed from first principles.

This is a low definition text which means that it is not necessary for the reader to memorize a large number of definitions. While there are many definitions, they are repeated over and over again; in fact, the book is designed so that a reader can open to almost any page and understand the material at hand without having to backtrack and awkwardly hunt for definitions of symbols and terms.

The philosophy of the exposition is to demonstrate the theory by simple, fully worked out examples.