Logo - springer
Slogan - springer

Birkhäuser - Birkhäuser Mathematics | Tata Lectures on Theta II - Jacobian theta functions and differential equations

Tata Lectures on Theta II

Jacobian theta functions and differential equations

Mumford, David

Originally published as volume 43 in the series: Progress in Mathematics

Reprint of the 1984 ed., XIV, 272 p. 21 illus.

A product of Birkhäuser Basel
Available Formats:
eBook
Information

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.

 
$49.99

(net) price for USA

ISBN 978-0-8176-4578-6

digitally watermarked, no DRM

Included Format: PDF

download immediately after purchase


learn more about Springer eBooks

add to marked items

Softcover
Information

Softcover (also known as softback) version.

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$69.99

(net) price for USA

ISBN 978-0-8176-4569-4

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

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.

Content Level » Research

Keywords » Divisor - Identity - Invariant - Riemann surfaces - algebra - algebraic geometry - equation - function - geometry - mathematical physics - mathematics

Related subjects » Birkhäuser Mathematics - Birkhäuser Physics

Table of contents 

An Elementary Construction of Hyperelliptic Jacobians.- Review of background in algebraic geometry.- Divisors on hyperelliptic curves.- Algebraic construction of the Jacobian of a hyperelliptic curve.- The translation-invariant vector fields.- Neumann’s dynamical system.- Tying together the analytic Jacobian and algebraic Jacobian.- Theta characteristics and the fundamental Vanishing Property.- Frobenius’ theta formula.- Thomae’s formula and moduli of hyperelliptic curves.- Characterization of hyperelliptic period matrices.- The hyperelliptic p-function.- The Korteweg-deVries dynamical system.- Fay’s Trisecant Identity for Jacobian theta functions.- The Prime Form E(x,y)..- Fay’s Trisecant Identity.- Corollaries of the identity.- Applications to solutions of differential equations.- The Generalized Jacobian of a Singular Curve and its Theta Function.- Resolution of algebraic equations by theta constants.- Resolution of algebraic equations by theta constants.

Popular Content within this publication 

 

Articles

Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Special Functions.