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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.
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.
From the reviews:
"This book provides a detailed exposition of Thomae's 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 Thomae's 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 Riemann's theory of theta functions. ... the 'elementary' approach which is chosen in the book makes it a nice development of Riemann's ideas and accessible to graduate students and young researchers." (Christophe Ritzenthaler, Zentralblatt MATH, Vol. 1222, 2011)
"This book provides a detailed exposition of Thomae's 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 Thomae's 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 Riemann's theory of theta functions. ... the 'elementary' approach which is chosen in the book makes it a nice development of Riemann's ideas and accessible to graduate students and young researchers." (Christophe Ritzenthaler, Zentralblatt MATH, Vol. 1222, 2011)