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" Eisenstein series and automorphic representations : "
Philipp Fleig [and three others].
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BL
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| Record Number
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839204
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| Title & Author
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Eisenstein series and automorphic representations : : with applications in string theory /\ Philipp Fleig [and three others].
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| Publication Statement
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Cambridge, United Kingdom ;New York, NY :: Cambridge University Press,, 2018.
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, ©2018
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| Series Statement
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Cambridge studies in advanced mathematics ;; 176
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xviii, 567 pages ;; 24 cm.
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| ISBN
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1107189926
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: 9781107189928
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Includes bibliographical references and index.
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| Contents
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Motivation and background -- Part One. Automorphic representations -- Preliminaries on p-adic and adelic technology -- Basic notions from lie algebras and lie groups -- Automorphic forms -- Automorphic representations and Eisenstein series -- Whittaker functions and fourier coefficients -- Fourier coefficients of Eisenstein series on SL (2, A) -- Langlands constant term formula -- Whittaker coefficients of Eisenstein series -- Analysing Eisenstein series and small representations -- Hecke theory and automorphic L-functions -- Theta correspondences -- Part Two. Applications in string theory -- Elements of string theory -- Automorphic scattering amplitudes -- Further occurrences of automorphic forms in string theory -- Part Three. Advanced topics -- Connections to the Langlands Program -- Whittaker functions, crystals and multiple Dirichlet series -- Automorphic forms on non-split real forms -- Extension to Kac-Moody groups.
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| Abstract
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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.
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Automorphic functions.
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Eisenstein series.
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String models.
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Automorphic functions.
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Eisenstein series.
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String models.
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| Dewey Classification
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512.7/3
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| LC Classification
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QA353.A9E47 2018
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| Added Entry
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Fleig, Philipp
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