Abelian Functions
Abel's Theorem and the Allied Theory of Theta Functions
Part of Cambridge Mathematical Library
 Author: H. F. Baker, St John's College, Cambridge
 Date Published: February 1996
 availability: Available
 format: Paperback
 isbn: 9780521498777
Paperback
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Classical algebraic geometry, inseparably connected with the names of Abel, Riemann, Weierstrass, Poincaré, 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.
Read more Classic book (almost 100 yrs old)
 Contains topics that have been quiet for decades but are now resurfacing in theoretical physics
 Introduction relates old theory to modern ideas
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×Product details
 Date Published: February 1996
 format: Paperback
 isbn: 9780521498777
 length: 724 pages
 dimensions: 234 x 156 x 37 mm
 weight: 1kg
 availability: Available
Table of Contents
1. The subject of investigation
2. The fundamental functions on a Riemann surface
3. The infinities of rational functions
4. Specification of a general form of Riemann's integrals
5. Certain forms of the fundamental equation of the Riemann surface
6. Geometrical investigations
7. Coordination of simple elements
8. Abel's theorem
9. Jacobi's inversion problem
10. Riemann's theta functions
11. The hyperelliptic case of Riemann's theta functions
12. A particular form of Riemann surface
13. Radical functions
14. Factorial functions
15. Relations concerning products of theta functions
16. A direct method of obtaining the equations relating theta functions
17. Theta relations with certain groups of characteristics
18. Transformation of periods
19. On systems of periods and on general Jacobian functions
20. Transformation of theta functions
21. Complex multiplication of theta functions
22. Degenerate Abelian integrals
Appendix 1. On algebraic curves in space
Appendix 2. On matrices.
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