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Tata Lectures on Theta II

Jacobian theta functions and differential equations

  • Book
  • © 2007


Part of the book series: Modern Birkhäuser Classics (MBC)

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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.

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Table of contents (18 chapters)

  1. An Elementary Construction of Hyperelliptic Jacobians

  2. Fay’s Trisecant Identity for Jacobian theta functions

  3. Resolution of algebraic equations by theta constants

Authors and Affiliations

  • Division of Applied Mathematics, Brown University, Providence, USA

    David Mumford

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