Tata Lectures on Theta II

Jacobian theta functions and differential equations

Häftad, Engelska, 2006

1 229 kr

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The second in a series of three volumes that survey the theory of theta functions, this volume emphasizes the special properties of the theta functions associated with compact Riemann surfaces and how they lead to solutions of the Korteweg-de-Vries equations.

Produktinformation

Utgivningsdatum2006-12-27
Mått155 x 235 x 25 mm
Vikt446 g
FormatHäftad
SpråkEngelska
SerieModern Birkhäuser Classics
Antal sidor272
FörlagBirkhauser Boston Inc
ISBN9780817645694

Tillhör följande kategorier

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.

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