Generalizations of Thomae's Formula for Zn Curves by Hershel M. Farkas (English)

Description: Generalizations of Thomae's Formula for Zn Curves by Hershel M. Farkas, Shaul Zemel Includes several focused proofs developed in a generalized context that is accessible to researchers in related mathematical fields such as algebraic geometry, complex analysis, and number theory. This book is suitable for mathematicians with an interest in complex analysis, algebraic geometry or number theory as well as physicists. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description Previous publications on the generalization of the Thomae formulae to Zn curves have emphasized the theorys 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 Thomaes 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. Notes The first monograph to study generalizations of the Thomae Formulae to Zn curvesProvides an introduction to the basic principles of compact Riemann surfaces, theta functions, algebraic curves, and branch pointsExamples 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 Back Cover 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. Table of Contents - 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. Review From the reviews:"This book provides a detailed exposition of Thomaes formula for cyclic covers of CP1, in the non-singular case and in the singular case for Zn curves of a particular shape. … This book is written for graduate students as well as young researchers … . In any case, the reader should be acquainted with complex analysis (in several variables), Riemann surfaces, and some elementary algebraic geometry. It is a very readable book. The theory is always illustrated with examples in a very generous mathematical style." (Juan M. Cerviño Mathematical Reviews, Issue 2012 f)"In the book under review, the authors present the background necessary to understand and then prove Thomaes formula for Zn curves. … The point of view of the book is to work out Thomae formulae for Zn curves from first principles, i.e. just using Riemanns theory of theta functions. … the elementary approach which is chosen in the book makes it a nice development of Riemanns ideas and accessible to graduate students and young researchers." (Christophe Ritzenthaler, Zentralblatt MATH, Vol. 1222, 2011) Review Quote From the reviews: "This book provides a detailed exposition of Thomaes formula for cyclic covers of CP1, in the non-singular case and in the singular case for Zn curves of a particular shape. ... This book is written for graduate students as well as young researchers ... . In any case, the reader should be acquainted with complex analysis (in several variables), Riemann surfaces, and some elementary algebraic geometry. It is a very readable book. The theory is always illustrated with examples in a very generous mathematical style." (Juan M. Cervio Mathematical Reviews, Issue 2012 f) "In the book under review, the authors present the background necessary to understand and then prove Thomaes formula for Zn curves. ... The point of view of the book is to work out Thomae formulae for Zn curves from first principles, i.e. just using Riemanns theory of theta functions. ... the elementary approach which is chosen in the book makes it a nice development of Riemanns ideas and accessible to graduate students and young researchers." (Christophe Ritzenthaler, Zentralblatt MATH, Vol. 1222, 2011) Feature 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 Details ISBN1441978461 Author Shaul Zemel Year 2010 ISBN-10 1441978461 ISBN-13 9781441978462 Format Hardcover Imprint Springer-Verlag New York Inc. Place of Publication New York, NY Country of Publication United States DEWEY 515.984 Short Title GENERALIZATIONS OF THOMAES FOR Language English Media Book Series Number 21 Publication Date 2010-11-24 Pages 354 DOI 10.1007/978-1-4419-7847-9 AU Release Date 2010-11-24 NZ Release Date 2010-11-24 US Release Date 2010-11-24 UK Release Date 2010-11-24 Publisher Springer-Verlag New York Inc. Edition Description 2011 ed. Series Developments in Mathematics Edition 2011th Alternative 9781461427582 Audience Professional & Vocational Illustrations XVII, 354 p. We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:96289763;

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