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＜E-Book＞
Generalizations of Thomae's Formula for Zn Curves / by Hershel M. Farkas, Shaul Zemel
(Developments in Mathematics. ISSN:2197795X ; 21)

Edition	1st ed. 2011.
Publisher	(New York, NY : Springer New York : Imprint: Springer)
Year	2011
Language	English
Size	XVII, 354 p : online resource
Authors	*Farkas, Hershel M author Zemel, Shaul author SpringerLink (Online service)
Subjects	LCSH:Algebraic geometry LCSH:Functions of complex variables LCSH:Special functions LCSH:Number theory FREE:Algebraic Geometry FREE:Functions of a Complex Variable FREE:Several Complex Variables and Analytic Spaces FREE:Special Functions FREE:Number Theory
Notes	- 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 HTTP:URL=https://doi.org/10.1007/978-1-4419-7847-9

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