A Window into Zeta and Modular Physics

Mathematical Sciences Research Institute

doi:10.1017/9780511762819

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.

- Aa Reduce text
- Aa Enlarge text

View selected items
Save to my bookmarks
Export citations
Download PDF (zip)
Save to Kindle
Save to Dropbox
Save to Google Drive
Save content to
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to .

To save content items to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Please be advised that item(s) you selected are not available.
You are about to save
Your Kindle email address

Please provide your Kindle email.

@free.kindle.com @kindle.com (service fees apply)

By using this service, you agree that you will only keep content for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services

Metrics

Total number of HTML views: 0

Total number of PDF views: 0 *

Loading metrics...

Total views: 0 *

Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.

Why this information is here

This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.

Accessibility Information

Accessibility compliance for the PDF of this book is currently unknown and may be updated in the future.

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.

Book description

Refine List

Actions for selected content:

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

Metrics

Full text views

Book summary page views

Accessibility standard: Unknown

Why this information is here

Accessibility Information

A Window into Zeta and Modular Physics

Book description

Refine List

Actions for selected content:

Save Search

Contents

Metrics

Full text views

Book summary page views

Accessibility standard: Unknown

Why this information is here

Accessibility Information