This volume uses a unified approach to representation theory and automorphic forms. It collects papers, written by leading mathematicians, that track recent progress in the expanding fields of representation theory and automorphic forms and their association with number theory and differential geometry. Topics include: Automorphic forms and distributions, modular forms, visible...(展开全部)

The theory of automorphic forms has seen dramatic developments in recent years. In particular, important instances of Langlands functoriality have been established. This volume presents three weeks of lectures from the IAS/Park City Mathematics Institute Summer School on automorphic forms and their applications. It addresses some of the general aspects of automorphic forms, as ...(展开全部)

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 fo...(展开全部)

Automorphic forms are an important complex analytic tool in number theory and modern arithmetic geometry. They played for example a vital role in Andrew Wiles's proof of Fermat's Last Theorem. This text provides a concise introduction to the world of automorphic forms using two approaches: the classic elementary theory and the modern point of view of adeles and representation t...(展开全部)

This classic monograph provides an overview of modern advances in representation theory from a geometric standpoint. A geometrically-oriented treatment of the subject is very timely and has long been desired, especially since the discovery of D-modules in the early 1980s and the quiver approach to quantum groups in the early 1990s. The techniques developed are quite general and...(展开全部)

The subject matter of these Notes is the interplay between the theory of automorphic forms and group representations. One goal is to interpret some recent developments in this area, most significantly the theory of Jacquet-Langlands, working out, whenever possible, explicit consequences and connections with the classical theory. Another goal is to collect as much information as...(展开全部)

L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This 2006 book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with a basic knowledge of classical analysis, complex variable theory, and algebra. Also within the...(展开全部)