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The Weierstrass Sigma Function in Higher Genus and Applications to Integrable Equations
Shigeki Matsutani
Page: 501
Format: pdf, ePub, mobi, fb2
ISBN: 9789819781621
Publisher: Springer Nature Singapore

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This book’s area is special functions of one or several complex variables. Special functions have been applied to dynamics and physics. Special functions such as elliptic or automorphic functions have an algebro-geometric nature. These attributes permeate the book. The “Kleinian sigma function”, or “higher-genus Weierstrass sigma function” generalizes the elliptic sigma function. It appears for the first time in the work of Weierstrass. Klein gave an explicit definition for hyperelliptic or genus-three curves, as a modular invariant analogue of the Riemann theta function on the Jacobian (the two functions are equivalent). H.F. Baker later used generalized Legendre relations for meromorphic differentials, and brought out the two principles of the theory: on the one hand, sigma uniformizes the Jacobian so that its (logarithmic) derivatives in one direction generate the field of meromorphic functions on the Jacobian, therefore algebraic relations among them generate the ideal of the Jacobian as a projective variety; on the other hand, a set of nonlinear PDEs (which turns out to include the “integrable hierarchies” of KdV type), characterize sigma. We follow Baker’s approach. There is no book where the theory of the sigma function is taken from its origins up to the latest most general results achieved, which cover large classes of curves. The authors propose to produce such a book, and cover applications to integrable PDEs, and the inclusion of related al functions, which have not yet received comparable attention but have applications to defining specific subvarieties of the degenerating family of curves. One reason for the attention given to sigma is its relationship to Sato's tau function and the heat equations for deformation from monomial curves. The book is based on classical literature and contemporary research, in particular our contribution which covers a class of curves whose sigma had not been found explicitly before.

On higher genus Weierstrass sigma-function - ADS
sigma-functions are constructed as a straightforward analog of a classical formula relating even and odd sigma-functions. In higher genus the even sigma- .
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Weierstrass Sigma Function in Higher Genus and Applications to Integrable Equations . book, and cover applications to integrable PDEs .
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The Weierstrass Sigma Function in Higher Genus and Applications .
This book's area is special functions of one or several complex variables. Special functions have been applied to dynamics and physics.
The Weierstrass Sigma Function in Higher Genus and Applications .
Book. $249.00 · eText. $239.00. The Weierstrass Sigma Function in Higher Genus and Applications to Integrable Equations. By: Shigeki Matsutani. Write A Review.
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This book's area is special functions of one or several complex variables. Special functions have been applied to dynamics and physics.
WeierstrassSigma - Wolfram Language Documentation
WeierstrassSigma[u, {g2, g3}] gives the Weierstrass sigma function WeierstrassSigma[u, {g2, g3}].
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This book explores the diverse types of Schrödinger equations . The Weierstrass Sigma Function in Higher Genus and Applications to Integrable Equations
The Weierstrass Sigma Function in Higher Genus and Applications .
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The Weierstrass Sigma Function in Higher Genus and Applications .
This book's area is special functions of one or several complex variables. Special functions have been applied to dynamics and physics. The "Kleinian sigma .
楕円関数の一般化とその応用— The Weierstrass sigma function in .
Weierstrass sigma function in higher genus and applications to integrable equations 4764907003, 9784764907003. 【応用を見据えた「楕円関数の延長としての超楕円 .
The Weierstrass Sigma Function in Higher Genus and Applications .
In this paper we introduce new definition of Hodge structures and show that R R -Hodge structures are determined by R R -linear operators .
The Weierstrass Sigma Function in Higher Genus and Applications .
This book's area is special functions of one or several complex variables. Special functions have been applied to dynamics and physics.