English
 
User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT
  Eisenstein series and automorphic representations

Fleig, P., Gustafsson, H. P. A., Kleinschmidt, A., & Persson, D. (in preparation). Eisenstein series and automorphic representations.

Item is

Basic

show hide
Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-6092-6 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-6093-4
Genre: Paper

Files

show Files
hide Files
:
1511.04265.pdf (Preprint), 4MB
Name:
1511.04265.pdf
Description:
File downloaded from arXiv at 2016-01-21 08:53
Visibility:
Public
MIME-Type / Checksum:
application/pdf / [MD5]
Technical Metadata:
Copyright Date:
-
Copyright Info:
-

Locators

show

Creators

show
hide
 Creators:
Fleig, Philipp1, Author              
Gustafsson, Henrik P. A., Author
Kleinschmidt, Axel2, Author              
Persson, Daniel, Author
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, ou_24014              
2Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

Content

show
hide
Free keywords: Mathematics, Number Theory, math.NT,High Energy Physics - Theory, hep-th,Mathematics, Representation Theory, math.RT
 Abstract: We provide an introduction to the theory of Eisenstein series and automorphic forms on real simple Lie groups G, emphasising the role of representation theory. It is useful to take a slightly wider view and define all objects over the (rational) adeles A, thereby also paving the way for connections to number theory, representation theory and the Langlands program. Most of the results we present are already scattered throughout the mathematics literature but our exposition collects them together and is driven by examples. Many interesting aspects of these functions are hidden in their Fourier coefficients with respect to unipotent subgroups and a large part of our focus is to explain and derive general theorems on these Fourier expansions. Specifically, we give complete proofs of Langlands' constant term formula for Eisenstein series on adelic groups G(A) as well as the Casselman--Shalika formula for the p-adic spherical Whittaker vector associated to unramified automorphic representations of G(Q_p). Somewhat surprisingly, all these results have natural interpretations as encoding physical effects in string theory. We therefore introduce also some basic concepts of string theory, aimed toward mathematicians, emphasising the role of automorphic forms. In addition, we explain how the classical theory of Hecke operators fits into the modern theory of automorphic representations of adelic groups, thereby providing a connection with some key elements in the Langlands program, such as the Langlands dual group LG and automorphic L-functions. Our treatise concludes with a detailed list of interesting open questions and pointers to additional topics where automorphic forms occur in string theory.

Details

show
hide
Language(s):
 Dates: 2015-11-13
 Publication Status: Not specified
 Pages: 326
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1511.04265
URI: http://arxiv.org/abs/1511.04265
 Degree: -

Event

show

Legal Case

show

Project information

show

Source

show