Eisenstein Series and Automorphic Representations - With Applications in String Theory

List of contents

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.

About the author

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.

Summary

Aimed at advanced students and active researchers in mathematics or theoretical physics, this book provides a detailed exposition of automorphic forms and representations, from the basics up to cutting-edge research topics at the interface between number theory and string theory.

Product details

• Authors: Philipp Fleig, Philipp Gustafsson Fleig, FLEIG PHILIPP, Henrik P. A. Gustafsson, Henrik P. A. (Stanford University Gustafsson, Axel Kleinschmidt, Axel (Max-Planck-Institut fur Gravitationsphysik Kleinschmidt, Daniel Persson, Daniel (Chalmers University of Technology Persson
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 30.06.2018
• EAN: 9781107189928
• ISBN: 978-1-107-18992-8
• No. of pages: 584
• Series: Cambridge Studies in Advanced Mathematics; Cambridge Studies in Advanced; Cambridge Studies in Advanced Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Miscellaneous; MATHEMATICS / Number Theory, Cosmology & the universe, Number Theory, Cosmology and the universe, Quantum physics (quantum mechanics & quantum field theory), Quantum physics (quantum mechanics and quantum field theory), Relativity physics, Mathematical physics