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Abelian Functions
Abel's Theorem and the Allied Theory of Theta Functions

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Part of Cambridge Mathematical Library

Author: H. F. Baker, St John's College, Cambridge

Date Published: February 1996
availability: Available
format: Paperback
isbn: 9780521498777

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About the Authors

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 the methods and ideas of topology, commutative algebra and Grothendieck's schemes enriched it and seemed to have replaced once and forever the somewhat naive language of classical algebraic geometry. This classic book, written in 1897, covers the whole of algebraic geometry and associated theories. Baker discusses the subject in terms of transcendental functions, and theta functions in particular. 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.
- 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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"...offers welcome historical insight into a key point in the history of algebraic geometry." John B. Little, Mathematical Reviews

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Product details
- Date Published: February 1996
- format: Paperback
- isbn: 9780521498777
- length: 724 pages
- dimensions: 228 x 153 x 38 mm
- weight: 0.993kg
- 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.
Look Inside
Author
H. F. Baker, St John's College, Cambridge
Foreword
Igor Krichever