Abelian Functions

Abel's Theorem and the Allied Theory of Theta Functions

AvH. F. Baker

Häftad, Engelska, 1995

Del i serien Cambridge Mathematical Library

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Beskrivning

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.

Produktinformation

Utgivningsdatum:1995-12-14
Mått:153 x 228 x 38 mm
Vikt:993 g
Format:Häftad
Språk:Engelska
Serie:Cambridge Mathematical Library
Antal sidor:724
Förlag:Cambridge University Press
Medarbetare:Krichever,Igor
ISBN:9780521498777

Utforska kategorier

Matematik inom Naturvetenskap och teknik

Recensioner i media

"...offers welcome historical insight into a key point in the history of algebraic geometry." John B. Little, Mathematical Reviews

Innehållsförteckning

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.