Abelian Functions

Abel's Theorem and the Allied Theory of Theta Functions

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Paperback | 12 February 1996

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724 Pages

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23.4 x 17.0 x 3.7

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Classical algebraic geometry, inseparably connected with the names of Abel, Riemann, Weierstrass, Poincare, Clebsch, Jacobi and other outstanding mathematicians of the last century, was mainly an analytical theory. In our century it has been enriched by the methods and ideas of topology, commutative algebra and Grothendieck's schemes seemed to have replaced once and forever the somewhat naive language of classical algebraic geometry. This book contains more than its modest title suggests. Written in 1897, its scope was as broad as it could possibly be, namely to cover the whole of algebraic geometry, and associated theories. The subject is discussed by Baker in terms of transcendental functions, and in particular theta functions. Many of the ideas put forward are of continuing relevance today, and some of the most exciting ideas from theoretical physics draw on work presented here.

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'... Baker covers an enormous amount of mathematics in an easy and efficient style.' Mathematika

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The subject of investigation
The fundamental functions on a Riemann surface
The infinities of rational functions
Specification of a general form of Riemann's integrals
Certain forms of the fundamental equation of the Riemann surface
Geometrical investigations
Coordination of simple elements
Abel's theorem
Jacobi's inversion problem
Riemann's theta functions
The hyperelliptic case of Riemann's theta functions
A particular form of Riemann surface
Radical functions
Factorial functions
Relations concerning products of theta functions
A direct method of obtaining the equations relating theta functions
Theta relations with certain groups of characteristics
Transformation of periods
On systems of periods and on general Jacobian functions
Transformation of theta functions
Complex multiplication of theta functions
Degenerate Abelian integrals
On algebraic curves in space
On matrices
Table of Contents provided by Publisher. All Rights Reserved.

Abelian Functions

Abel's Theorem and the Allied Theory of Theta Functions

At a Glance

Paperback

Industry Reviews

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How to return your order

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