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

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Cambridge University Press, 1897 - Mathematics - 684 pages
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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 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.
 

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Contents

CHAPTER I
1
CHAPTER II
14
Expression of a rational function by integrals of the second kind
24
CHAPTER IV
47
Illustrative example for a surface of four sheets 53
53
Definition of derived set of special functions 0 _ 6164
61
Algebraical form of elementary integral of the third kind in general 6870
68
The discriminant of the fundamental set of integral functions
74
CHAPTER XIII
374
CHAPTER XIV
393
Alternative investigation of everywhere finite factorial functions
401
Connection of theory of factorial functions with theory of auto
439
CHAPTER XVI
471
The goiieral formula obtained by multiplying any number
477
CHAPTER XVII
486
CHAPTER XVIII
528

CERTAIN FORMS OF THE FUNDAMENTAL EQUATION OF THE RIEMANN SURFACE
80
7279
96
CHAPTER VI
113
CHAPTER VII
168
CHAPTER VIII
207
CHAPTER IX
235
CHAPTER X
246
Factorial integrals of the primary and associated systems 397 398
256
CHAPTER XI
296
CHAPTER XII
343
PAGES
544
case Weierstrasss number notation for halfinteger charac
569
Sketch of the results obtained References to the literature 599
599
CHAPTER XXI
629
CHAPTER XXII
657
APPENDIX I
664
INDEX OF AUTHORS QUOTED 677
677
254 Definition of a factorial function including radical function
683
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