Eisenstein series and automorphic representations: with applications in string theory

By:

Fleig, Philipp

Contributor(s):

Series: Cambridge studies in advanced mathematics ; 176Publication details: Cambridge University Press, 2018. Cambridge:Description: xviii, 567 p. : ill. ; hb, 24 cmISBN:

9781107189928

Subject(s):

DDC classification:

512.73 FLE

Summary: 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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Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar General Stacks	General	512.73 FLE (Browse shelf(Opens below))	1	Available		030088

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Previous	512.7209 CLE Are numbers real: the uncanny relationships between maths and the physical world	512.73 APO Introduction to analytic number theory	512.73 APO Introduction to analytic number theory	512.73 FLE Eisenstein series and automorphic representations: with applications in string theory	512.73 GEL Transcendental and algebraic numbers	512.73 HAL Sieve methods	512.73 HAR Prime-detecting Sieves	Next

Includes bibliographical references and index.

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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