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A Window into Zeta and Modular Physics : Mathematical Sciences Research Institute Publications - Klaus Kirsten

A Window into Zeta and Modular Physics

Mathematical Sciences Research Institute Publications

By: Klaus Kirsten (Editor), Floyd L. Williams (Editor)


Published: 1st June 2010
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This book provides an introduction to (1) various zeta functions (for example, Riemann, Hurwitz, Barnes, Epstein, Selberg, and Ruelle), including graph zeta functions; (2) modular forms (Eisenstein series, Hecke and Dirichlet L-functions, Ramanujan's tau function, and cusp forms); and (3) vertex operator algebras (correlation functions, quasimodular forms, modular invariance, rationality, and some current research topics including higher genus conformal field theory). Various concrete applications of the material to physics are presented. These include Kaluza-Klein extra dimensional gravity, Bosonic string calculations, an abstract Cardy formula for black hole entropy, Patterson-Selberg zeta function expression of one-loop quantum field and gravity partition functions, Casimir energy calculations, atomic Schroedinger operators, Bose-Einstein condensation, heat kernel asymptotics, random matrices, quantum chaos, elliptic and theta function solutions of Einstein's equations, a soliton-black hole connection in two-dimensional gravity, and conformal field theory.

Introductory Lectures:
Lectures on zeta functions, L-functions and modular forms with some physical applications
Basic zeta functions and some applications in physics
Zeta functions and chaos
Vertex operators and modular forms
Research Lectures:
Applications of elliptic and theta functions to Friedmann-Robertson-LemaƮtre-Walker cosmology with cosmological constant
Integrable systems and 2D gravitation: how a soliton illuminates a black hole
Functional determinants in higher dimensions using contour integrals
The role of the Patterson-Selberg zeta function of a hyperbolic cylinder in three-dimensional gravity with a negative cosmological constant
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521199308
ISBN-10: 0521199301
Series: Mathematical Sciences Research Institute Publications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 360
Published: 1st June 2010
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 24.3 x 16.5  x 2.7
Weight (kg): 0.63