A Window into Zeta and Modular Physics

Mathematical Sciences Research Institute

doi:10.1017/9780511762819

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L.Williams, Floyd 2015. Zeta Function Expression of Spin Partition Functions on Thermal AdS3. Mathematics, Vol. 3, Issue. 3, p. 653.

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Morales-Almazan, Pedro 2016. Casimir energy for perturbed surfaces of revolution. International Journal of Modern Physics A, Vol. 31, Issue. 09, p. 1650044.

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Edited by Klaus Kirsten, Baylor University, Texas, Floyd L. Williams, University of Massachusetts, Amherst
Mathematical Sciences Research Institute

Publisher:: Cambridge University Press
Online publication date:: May 2025
Print publication year:: 2010
Online ISBN:: 9780511762819
DOI:: https://doi.org/10.1017/9780511762819

Subjects:: Mathematics, Mathematical Physics, Real and Complex Analysis, Number Theory
Series:: Mathematical Sciences Research Institute Publications (57)

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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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A Window into Zeta and Modular Physics

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

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Contents

Frontmatter
pp i-vi

Contents
pp vii-viii

Introduction
pp 1-6

Lectures on zeta functions, L-functions and modular forms with some physical applications
pp 7-100

Basic zeta functions and some applications in physics
pp 101-144

Zeta functions and chaos
pp 145-182

Vertex operators and modular forms
pp 183-278

Applications of elliptic and theta functions to Friedmann–Robertson–Lemaître–Walker cosmology with cosmological constant
pp 279-294

Integrable systems and 2D gravitation: How a soliton illuminates a black hole
pp 295-306

Functional determinants in higher dimensions using contour integrals
pp 307-328

The role of the Patterson–Selberg zeta function of a hyperbolic cylinder in three-dimensional gravity with a negative cosmological constant
pp 329-351

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A Window into Zeta and Modular Physics

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