Philipp Fleig

Eisenstein Series and Automorphic Representations (eBook, PDF)

With Applications in String Theory

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 5. Juli 2018
• Englisch
• ISBN-13: 9781108118996
• Artikelnr.: 54059737

Autorenporträt

Philipp Fleig is a Postdoctoral Researcher at the Max-Planck-Institut für Dynamik und Selbstorganisation, Germany.

Inhaltsangabe

1. Motivation and background
Part I. Automorphic Representations: 2. Preliminaries on p-adic and adelic technology
3. Basic notions from Lie algebras and Lie groups
4. Automorphic forms
5. Automorphic representations and Eisenstein series
6. Whittaker functions and Fourier coefficients
7. Fourier coefficients of Eisenstein series on SL(2, A)
8. Langlands constant term formula
9. Whittaker coefficients of Eisenstein series
10. Analysing Eisenstein series and small representations
11. Hecke theory and automorphic L-functions
12. Theta correspondences
Part II. Applications in String Theory: 13. Elements of string theory
14. Automorphic scattering amplitudes
15. Further occurrences of automorphic forms in string theory
Part III. Advanced Topics: 16. Connections to the Langlands program
17. Whittaker functions, crystals and multiple Dirichlet series
18. Automorphic forms on non-split real forms
19. Extension to Kac-Moody groups
Appendix A. SL(2, R) Eisenstein series and Poisson resummation
Appendix B. Laplace operators on G/K and automorphic forms
Appendix C. Structure theory of su(2, 1)
Appendix D. Poincaré series and Kloosterman sums
References
Index.