A Window Into Zeta and Modular Physics

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Klaus Kirsten, Floyd L. Williams
Cambridge University Press, May 24, 2010 - Mathematics - 351 pages
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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 Schrödinger 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.
  

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Contents

Basic zeta functions and some applications in physics
101
Zeta functions and chaos
145
Analytic continuation and functional equation of
146
Vertex operators and modular forms
183
Research Lectures
279
How a soliton illuminates a black hole
295
Functional determinants in higher dimensions using contour integrals
307
since j1nsj D 1nRes 1n1Cı on Sı with
319
The role of the PattersonSelberg zeta function of a hyperbolic cylinder
329
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About the author (2010)

Dr Klaus Kirsten is a Professor of Mathematics at Baylor University. He is the author of Spectral Functions in Mathematics and Physics (2002) and more than 100 refereed articles in international journals.

Floyd L. Williams is Emeritus Professor of Mathematics at the University of Massachusetts, Amherst. He has edited or authored 27 books and published 78 research papers in math and physics journals. Williams has given more than 100 invited lectures at numerous universities in America and in some 20 different countries around the world.

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