Preface

Summary

The theory of automorphic forms, rightly or wrongly, has a reputation of being difficult for the student. I felt that there was a need for a book that would present the subject in a style that was accessible yet based on complete proofs and revealed clearly the uniqueness principles that underlie the basic constructions. I have been lecturing on automorphic forms and representation theory at Stanford and the Mathematical Sciences Research Institute since 1990, and this book is the end result.

The level of this book is intermediate between an advanced textbook and a monograph. I hope that it will be interesting to experts as well as graduate students. Its aim is to cover a substantial portion of the theory of automorphic forms on GL(2). Both the “classical” and “representation theoretic” viewpoints are covered.

There are significant omissions from my treatment, most seriously the Selberg trace formula. It has not been my aim to achieve complete coverage of the topics treated or to write a reference book. I feel that the existing reference material is adequate, and that it was not feasible to cover any single topic with the thoroughness I would have liked. I hope that the reader will begin studying the reference material (such as the Corvallis volume (Borel and Casselman, 1979) and above all Jacquet and Langlands (1970)) in the course of reading this book.