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Abelian Functions

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

Part of Cambridge Mathematical Library

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

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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.

    • 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.

  • Author

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

    Foreword

    Igor Krichever

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