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  3. Automorphic Forms and Representations
  • Cited by 261
Publisher:
Cambridge University Press
Online publication date:
December 2009
Print publication year:
1997
Online ISBN:
9780511609572
DOI:
https://doi.org/10.1017/CBO9780511609572
Subjects:
Mathematics (general), Mathematics, Number Theory, Algebra
Series:
Cambridge Studies in Advanced Mathematics (55)
Information

Book description

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.

Reviews

‘This important textbook closes a gap in the existing literature, for it presents the ‘representation theoretic’ viewpoint of the theory of automorphic forms on GL(2) … it will become a stepping stone for many who want to study the Corvallis Proceedings or the Lecture Notes by H. Jaquet and R. Langlands or seek a pathway to R. Langland’s conjectures.’

Source: Monatshefte für Mathematik

‘Students and researchers will find the book an understandable and penetrating treatment of a beautiful theory.’

Source: European Mathematical Society

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