Developments in Mathematics

By: Hershel M. Farkas, Shaul Zemel

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Hardcover | 24 November 2010

At a Glance

Hardcover
374 Pages

Dimensions(cm)
23.5 x 15.88 x 1.91

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$169.75

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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 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.

Industry Reviews

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 Z_n 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. Cervi±o 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 Z_ncurves. ... The point of view of the book is to work out Thomae formulae for Z_ncurves 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)

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