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 inrelated mathematical fields such as algebraic geometry, complex analysis, andnumber 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 branchpoints Examples support the theory and reveal the broad applicability of thistheory to numerous other disciplines including conformal field theory, low dimensional topology, the theory of special functions INDICE: - Introduction.- 1. Riemann Surfaces.- 2. Z n Curves.- 3. Examplesof 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.-AppendixA. 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.
- ISBN: 978-1-4419-7846-2
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 354
- Fecha Publicación: 29/11/2010
- Nº Volúmenes: 1
- Idioma: Inglés
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- ÁLGEBRA