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The Weierstrass Sigma Function in Higher Genus and Applications to Integrable Equations by Shigeki Matsutani
- 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.
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.
7 - Bergman Tau-Function: From Einstein Equations and Dubrovin .
These tau-functions are natural generalizations of Dedekind's eta-function to higher genus. Book: Integrable Systems and Algebraic Geometry; Online .
Weierstrass Sigma Function in Higher Genus and Applications to .
This book's area is special functions of one or several complex variables. Special functions have been applied to dynamics and physics.
Weierstrass elliptic functions and ordinary differential equations
This sounds very attractive to me but I have been unable to find references to unpack exactly what is meant. Does a genus 1 ODE mean one whose .
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[1201.3961] On higher genus Weierstrass sigma-function - arXiv
The goal of this paper is to propose a new way to generalize the Weierstrass sigma-function to higher genus Riemann surfaces.
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. Special functions such .
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The Weierstrass Sigma Function in Higher Genus and Applications to Integrable Equations · Classical Fine Potential Theory · Homogenization Algebras and .
The Weierstrass Sigma Function in Higher Genus and Applications .
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 .
Springer Monographs in Mathematics-The Weierstrass Sigma . - Bol
Springer Monographs in Mathematics-The Weierstrass Sigma Function in Higher Genus and Applications to Integrable Equations ; Bindwijze : Hardcover ; Samenvatting.
Springer monographs in mathematics - CERN Library Catalogue
BOOK. The Weierstrass Sigma Function in Higher Genus and Applications to Integrable Equations. Matsutani, Shigeki. 2025 - Edition 1st. Springer. E- .
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.
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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