Generalizations of Thomae's Formula for Zn Curves

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 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.

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

Inhalt

• Introduction.- 1. Riemann Surfaces.- 2. Zn Curves.- 3. Examples of Thomae Formulae.- 4. Thomae Formulae for Nonsingular Zn Curves.- 5. Thomae Formulae for Singular Zn Curves.-6. Some More Singular Zn 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.