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Table of contents (18 chapters)
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Front Matter
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An Elementary Construction of Hyperelliptic Jacobians
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Fay’s Trisecant Identity for Jacobian theta functions
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Resolution of algebraic equations by theta constants
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Back Matter
About this book
The second in a series of three volumes surveying the theory of theta functions, this volume gives emphasis to the special properties of the theta functions associated with compact Riemann surfaces and how they lead to solutions of the Korteweg-de-Vries equations as well as other non-linear differential equations of mathematical physics.
This book presents an explicit elementary construction of hyperelliptic Jacobian varieties and is a self-contained introduction to the theory of the Jacobians. It also ties together nineteenth-century discoveries due to Jacobi, Neumann, and Frobenius with recent discoveries of Gelfand, McKean, Moser, John Fay, and others.
A definitive body of information and research on the subject of theta functions, this volume will be a useful addition to individual and mathematics research libraries.
Authors and Affiliations
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Division of Applied Mathematics, Brown University, Providence, USA
David Mumford
Bibliographic Information
Book Title: Tata Lectures on Theta II
Book Subtitle: Jacobian theta functions and differential equations
Authors: David Mumford
Series Title: Modern Birkhäuser Classics
DOI: https://doi.org/10.1007/978-0-8176-4578-6
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Boston 2007
Softcover ISBN: 978-0-8176-4569-4Published: 27 December 2006
eBook ISBN: 978-0-8176-4578-6Published: 15 April 2012
Series ISSN: 2197-1803
Series E-ISSN: 2197-1811
Edition Number: 1
Number of Pages: XIV, 272
Additional Information: Originally published as volume 43 in the series: Progress in Mathematics
Topics: Special Functions, Algebraic Geometry, Mathematical Methods in Physics, Functions of a Complex Variable, Algebraic Topology, Partial Differential Equations