Generalizations of Thomae's Formula for Zn Curves

  • Hershel M. Farkas
  • Shaul Zemel

Part of the Developments in Mathematics book series (DEVM, volume 21)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Hershel M. Farkas, Shaul Zemel
    Pages 1-30
  3. Hershel M. Farkas, Shaul Zemel
    Pages 31-74
  4. Hershel M. Farkas, Shaul Zemel
    Pages 75-141
  5. Hershel M. Farkas, Shaul Zemel
    Pages 143-182
  6. Hershel M. Farkas, Shaul Zemel
    Pages 183-232
  7. Hershel M. Farkas, Shaul Zemel
    Pages 233-288
  8. Back Matter
    Pages 289-354

About this book

Introduction

This book provides a comprehensive overview of the theory of theta functions, as applied to compact Riemann surfaces, as well as the necessary background for understanding and proving the Thomae formulae.

The exposition examines the properties of a particular class of compact Riemann surfaces, i.e., the Zn curves, and thereafter focuses on how to prove the Thomae formulae, which give a relation between the algebraic parameters of the Zn curve, and the theta constants associated with the Zn curve.

Graduate students in mathematics will benefit from the classical material, connecting Riemann surfaces, algebraic curves, and theta functions, while young researchers, whose interests are related to complex analysis, algebraic geometry, and number theory, will find new rich areas to explore. Mathematical physicists and physicists with interests also in conformal field theory will surely appreciate the beauty of this subject.

Keywords

Algebraic Curves Algebraic Geometry Branch Points Conformal Field Theory Hypereliptic Curves Riemann Surfaces Theta Constants Theta Functions Thomae Formulae Zn Curves

Authors and affiliations

  • Hershel M. Farkas
    • 1
  • Shaul Zemel
    • 2
  1. 1., Einstein Institute of MathematicsHebrew University of JerusalemJerusalemIsrael
  2. 2.Einstein Institute of MathematicsHebrew University of JerusalemJerusalemIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-7847-9
  • Copyright Information Springer Science + Business Media, LLC 2011
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-7846-2
  • Online ISBN 978-1-4419-7847-9
  • Series Print ISSN 1389-2177
  • About this book