A Window into Zeta and Modular Physics Hardback
Edited by Klaus (Baylor University, Texas) Kirsten, Floyd L. (University of Massachusetts, Amherst) Williams
Part of the Mathematical Sciences Research Institute Publications series
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.
- Format: Hardback
- Pages: 360 pages
- Publisher: Cambridge University Press
- Publication Date: 24/05/2010
- Category: Applied mathematics
- ISBN: 9780521199308