Automorphic Forms & Representations (Cambridge Studies in Advanced Mathematics)

This book covers both the classical and representation theoretic views of automorphic forms in a style that 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, and examines this subject matter from many different and complementary viewpoints. Researchers as well as students in algebra and number theory will find this a valuable guide to a notoriously difficult subject.

The theory of automorphic forms is a cornerstone in modern number theory. It was an essential ingredient of the proof of Fermat's Last Theorem. However, in large part because of the lack of a suitable text this theory has been difficult for students to learn. This book addresses that difficulty. It begins with extensive foundational material and builds to topics on the resear ch frontier, such as the Langlands conjectures and the Weil representation.Researchers as well as students will find this a valuable guide to a notoriously difficult subject.