Automorphic Forms and Representations

This book takes advanced graduate students from the foundations to topics on the research frontier.

The theory of automorphic forms is a cornerstone in modern number theory, an essential ingredient of the proof of Fermat's Last Theorem. This book presents the subject in a style which is accessible to graduate students entering the field, yet includes topics on the research frontier.Intermediate in level between an advanced textbook and a monograph, this book covers both the classical and representation theoretic views of automorphic forms in a style which is accessible to graduate students entering the field. The treatment is based on complete proofs, which reveal the uniqueness principles underlying the basic constructions. The book features extensive foundational material on the representation theory of GL(1) and GL(2) over local fields, the theory of automorphic representations, L-functions and advanced topics such as the Langlands conjectures, the Weil representation, the Rankin–Selberg method and the triple L-function, examining this subject matter from many different and complementary viewpoints. Researchers as well as students will find this a valuable guide to a notoriously difficult subject.