Overview
- The first monograph to study generalizations of the Thomae Formulae to Zn curves
- Provides an introduction to the basic principles of compact Riemann surfaces, theta functions, algebraic curves, and branch points
- Examples support the theory and reveal the broad applicability of this theory to numerous other disciplines including conformal field theory, low dimensional topology, the theory of special functions
Part of the book series: Developments in Mathematics (DEVM, volume 21)
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Table of contents (6 chapters)
Keywords
About this book
Previous publications on the generalization of the Thomae formulae to Zn curves have emphasized the theory's implications in mathematical physics and depended heavily on applied mathematical techniques. This book redevelops these previous results demonstrating how they can be derived directly from the basic properties of theta functions as functions on compact Riemann surfaces.
"Generalizations of Thomae's Formula for Zn Curves" includes several refocused proofs developed in a generalized context that is more accessible to researchers in related mathematical fields such as algebraic geometry, complex analysis, and number theory.
This book is intended for mathematicians with an interest in complex analysis, algebraic geometry or number theory as well as physicists studying conformal field theory.
Reviews
From the reviews:
“This book provides a detailed exposition of Thomae’s formula for cyclic covers of CP1, in the non-singular case and in the singular case for Zn curves of a particular shape. … This book is written for graduate students as well as young researchers … . In any case, the reader should be acquainted with complex analysis (in several variables), Riemann surfaces, and some elementary algebraic geometry. It is a very readable book. The theory is always illustrated with examples in a very generous mathematical style.” (Juan M. Cerviño Mathematical Reviews, Issue 2012 f)
“In the book under review, the authors present the background necessary to understand and then prove Thomae’s formula for Zn curves. … The point of view of the book is to work out Thomae formulae for Zn curves from ‘first principles’, i.e. just using Riemann’s theory of theta functions. … the ‘elementary’ approach which is chosen in the book makes it a nice development of Riemann’s ideas and accessible to graduate students and young researchers.” (Christophe Ritzenthaler, Zentralblatt MATH, Vol. 1222, 2011)
Authors and Affiliations
Bibliographic Information
Book Title: Generalizations of Thomae's Formula for Zn Curves
Authors: Hershel M. Farkas, Shaul Zemel
Series Title: Developments in Mathematics
DOI: https://doi.org/10.1007/978-1-4419-7847-9
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media, LLC 2011
Hardcover ISBN: 978-1-4419-7846-2Published: 24 November 2010
Softcover ISBN: 978-1-4614-2758-2Published: 27 December 2012
eBook ISBN: 978-1-4419-7847-9Published: 10 November 2010
Series ISSN: 1389-2177
Series E-ISSN: 2197-795X
Edition Number: 1
Number of Pages: XVII, 354
Topics: Algebraic Geometry, Functions of a Complex Variable, Several Complex Variables and Analytic Spaces, Special Functions, Number Theory