A Window into Zeta and Modular Physics
Part of Mathematical Sciences Research Institute Publications
 Editors:
 Klaus Kirsten, Baylor University, Texas
 Floyd L. Williams, University of Massachusetts, Amherst
 Date Published: January 2014
 availability: Available
 format: Paperback
 isbn: 9781107633933
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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 Lfunctions, 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 KaluzaKlein extra dimensional gravity, Bosonic string calculations, an abstract Cardy formula for black hole entropy, PattersonSelberg zeta function expression of oneloop quantum field and gravity partition functions, Casimir energy calculations, atomic Schrödinger operators, BoseEinstein condensation, heat kernel asymptotics, random matrices, quantum chaos, elliptic and theta function solutions of Einstein's equations, a solitonblack hole connection in twodimensional gravity, and conformal field theory.
Read more The book consists of lectures that are part of the distinguished series of MSRI workshops
 A serious attempt is made to bridge various gaps between mathematics and physics where, in particular, students and nonexperts are targeted
 Links and interesting interconnections between seemingly unrelated topics in these fields (mathematics and physics) are consistently explored, with a fair amount of detail and exposition
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×Product details
 Date Published: January 2014
 format: Paperback
 isbn: 9781107633933
 length: 360 pages
 dimensions: 234 x 156 x 19 mm
 weight: 0.5kg
 availability: Available
Table of Contents
Part I. Introductory Lectures:
1. Lectures on zeta functions, Lfunctions and modular forms with some physical applications Floyd L. Williams
2. Basic zeta functions and some applications in physics Klaus Kirsten
3. Zeta functions and chaos Audrey Terras
4. Vertex operators and modular forms Geoffrey Mason and Michael Tuite
Part II. Research Lectures:
5. Applications of elliptic and theta functions to FriedmannRobertsonLemaîtreWalker cosmology with cosmological constant Jennie D'Ambroise
6. Integrable systems and 2D gravitation: how a soliton illuminates a black hole Shabnam Beheshti
7. Functional determinants in higher dimensions using contour integrals Klaus Kirsten
8. The role of the PattersonSelberg zeta function of a hyperbolic cylinder in threedimensional gravity with a negative cosmological constant Floyd L. Williams.
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