Generalizations of Thomae's Formula for Zn Curves [electronic resource] / by Hershel M. Farkas, Shaul Zemel.
By: Farkas, Hershel M [author.].
Contributor(s): Zemel, Shaul [author.] | SpringerLink (Online service).
Material type:
BookSeries: Developments in Mathematics, Diophantine Approximation: Festschrift for Wolfgang Schmidt: 21Publisher: New York, NY : Springer New York, 2011Description: XVII, 354 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9781441978479.Subject(s): Mathematics | Geometry, algebraic | Functions of complex variables | Differential equations, partial | Functions, special | Number theory | Mathematics | Algebraic Geometry | Functions of a Complex Variable | Several Complex Variables and Analytic Spaces | Special Functions | Number TheoryDDC classification: 516.35 Online resources: Click here to access online - 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.
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.
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