Abelian functions : Abel's theorem and the allied theory of theta functions
著者
書誌事項
Abelian functions : Abel's theorem and the allied theory of theta functions
（Cambridge mathematical library）
Cambridge University Press, 1995
- : pbk
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注記
"First published 1897"--T.p. verso
Includes bibliographical references and indexes
内容説明・目次
内容説明
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.
目次
- 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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