Eisenstein Series and Automorphic Representations: With Applications in String Theory

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Philipp Fleig Henrik P. A. Gustafsson (Stanford University, California)

Eisenstein Series and Automorphic Representations

With Applications in String Theory

Philipp Fleig, Henrik P. A. Gustafsson (Stanford University, California), Axel Kleinschmidt (Max-Planck-Institut für Gravitationsphysik, Germany) , Daniel Persson (Chalmers University of Technology, Gothenberg)

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English

Cambridge University Press
05 July 2018

Number theory; Cosmology & the universe; Quantum physics (quantum mechanics & quantum field theory); Relativity physics; Mathematical physics

Series: Cambridge Studies in Advanced Mathematics

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.

By: Philipp Fleig, Henrik P. A. Gustafsson (Stanford University, California), Axel Kleinschmidt (Max-Planck-Institut für Gravitationsphysik, Germany), Daniel Persson (Chalmers University of Technology, Gothenberg)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: 176
Dimensions: Height: 235mm, Width: 157mm, Spine: 38mm
Weight: 920g
ISBN: 9781107189928
ISBN 10: 1107189926
Series: Cambridge Studies in Advanced Mathematics
Pages: 584
Publication Date: 05 July 2018
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Philipp Fleig is a Postdoctoral Researcher at the Max-Planck-Institut für Dynamik und Selbstorganisation, Germany. Henrik P. A. Gustafsson is a Postdoctoral Researcher in the Department of Mathematics at Stanford University, California. Axel Kleinschmidt is a Senior Scientist at the Max-Planck-Institut für Gravitationsphysik, Germany (Albert Einstein Institute) and at the International Solvay Institutes, Brussels. Daniel Persson is an Associate Professor in the Department of Mathematical Sciences at Chalmers University of Technology, Gothenburg.

Reviews for Eisenstein Series and Automorphic Representations: With Applications in String Theory

'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, MathSciNet '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, MathSciNet