This book provides a comprehensive overview of the theory of theta functions, and the necessary background for understanding and proving the Thomae formulae and their relationship to the Zn curves.
The book is intended for graduate students in mathematics studying complex analysis, algebraic geometry, and number theory as well as mathematical physicists and physicists studying conformal field theory.

Previous publications on the generalization of the Thomae formulae to Z n 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 Z n 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.

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

Klappentext
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.

Inhalt

• Introduction.- 1. Riemann Surfaces.- 2. Z n Curves.- 3. Examples of Thomae Formulae.- 4. Thomae Formulae for Nonsingular Z n Curves.- 5. Thomae Formulae for Singular Z n Curves.-6. Some More Singular Z n Curves.-Appendix A. Constructions and Generalizations for the Nonsingular and Singular Cases.-Appendix B. The Construction and Basepoint Change Formulae for the Symmetric Equation Case.-References.-List of Symbols.-Index.