Price loading...

The Weierstrass Sigma Function in Higher Genus and Applications to Integrable Equations (Springer Monographs in Mathematics)

Algebra

Price data last checked 103 day(s) ago - refreshing...

View at Amazon

Price History & Forecast

No Price Data Available

Price history will appear here once data is collected from Amazon.

Price Distribution

No price data available for histogram

Description

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.

Product Specifications

Format: hardcover
ASIN: 9819781620
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Algebra
Domain: Amazon UK
Release Date: 26 March 2025
Listed Since: 16 August 2024

Barcode

No barcode data available

The Weierstrass Sigma Function in Higher Genus and Applications to Integrable Equations (Springer Monographs in Mathematics)

Price History & Forecast

No Price Data Available

Price Distribution

Description

Product Specifications

Barcode

Similar Products You Might Like

Analytic Partial Differential Equations: 359 (Grundlehren der mathematischen Wissenschaften, 359)

Springer - The Beltrami Equation: A Geometric Approach, Vol 26

Theory and Applications of Abstract Semilinear Cauchy Problems: 201 (Applied Mathematical Sciences, 201)

Elementary Geometry in Hyperbolic Space: 11 (De Gruyter Studies in Mathematics, 11)

Multi-Valued Variational Inequalities and Inclusions (Springer Monographs in Mathematics)

Parabolicity, Volterra Calculus, and Conical Singularities

Curvature Measures of Singular Sets (Springer Monographs in Mathematics)

Curvature Measures of Singular Sets (Springer Monographs in Mathematics)

Nevanlinna Theory and Complex Differential Equations: 15 (De Gruyter Studies in Mathematics, 15)

Nonlinear Analysis, Differential Equations, and Applications: 173 (Springer Optimization and Its Applications, 173)

Academic Press - Hypergeometric & Supertrigonometric Functions

De Gruyter Holomorphic Functions of Several Variables - Math Book

Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group (Springer Monographs in Mathematics)

Special Functions in Physics with MATLAB

Zeta Functions Of Reductive Groups And Their Zeros (Algebraic Geometry Algebraic T)

Ordinary Differential Equations: An Introduction to Nonlinear Analysis: 13 (De Gruyter Studies in Mathematics, 13)

Funktionentheorie: Komplexe Analysis in einer Veränderlichen (vieweg studium; Aufbaukurs Mathematik)

Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers: 28 (Algorithms and Computation in Mathematics, 28)

C*-Algebras and Elliptic Operators in Differential Topology: 192 (Translations of Mathematical Monographs)

The Geometry of Higher-Order Hamilton Spaces: Applications to Hamiltonian Mechanics: 132 (Fundamental Theories of Physics, 132)

Basic Algebraic Geometry (Springer Study Edition)

Multivalued Differential Equations: 1 (De Gruyter Series in Nonlinear Analysis & Applications, 1)

Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations: 3 (De Gruyter Series in Nonlinear Analysis & Applications, 3)

Theory of Hypergeometric Functions (Springer Monographs in Mathematics)