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Eisenstein Series and Automorphic Representations

Book description

This introduction to automorphic forms on adelic groups G(A) emphasises the role of representation theory. The exposition is driven by examples, and collects and extends many results scattered throughout the literature, in particular the Langlands constant term formula for Eisenstein series on G(A) as well as the Casselman–Shalika formula for the p-adic spherical Whittaker function. This book also covers more advanced topics such as spherical Hecke algebras and automorphic L-functions. Many of these mathematical results have natural interpretations in string theory, and so some basic concepts of string theory are introduced with an emphasis on connections with automorphic forms. Throughout the book special attention is paid to small automorphic representations, which are of particular importance in string theory but are also of independent mathematical interest. Numerous open questions and conjectures, partially motivated by physics, are included to prompt the reader's own research.

Reviews

'This book provides a bridge between two very active and important parts of mathematics and physics, namely the theory of automorphic forms on reductive groups and string theory. The authors have masterfully presented both aspects and their connections, and have provided examples and details at all levels to make the book available to a large readership, including non-experts in both fields. This is a valuable contribution and a welcoming text for graduate students as well.’

Freydoon Shahidi - Purdue University, Indiana

'The book is a valuable addition to the literature, and it may inspire more exchange between mathematics and physics at an advanced level.'

Anton Deitmar Source: MathSciNet

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