## Abelian Functions: Abel's Theorem and the Allied Theory of Theta FunctionsClassical 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. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### 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 |

683 | |

### Other editions - View all

Abelian Functions: Abel's Theorem and the Allied Theory of Theta Functions Henry Frederick Baker,H. F. Baker No preview available - 1897 |

Abelian Functions: Abel's Theorem and the Allied Theory of Theta Functions Henry Frederick Baker,H. F. Baker No preview available - 1897 |

### Common terms and phrases

Abel's theorem adjoint polynomial algebraic algebraic curve arbitrary constants arbitrary place argument branch places Chap Chapter condition considered coresidual corresponding Crelle cubic surface denote depends determined differential coefficients dimension double points equal essential singularities exists expression factor factorial function finite number finite places follows formula function of order fundamental equation given Hence hyperelliptic hyperelliptic surface infinitesimal infinity integral function integral polynomial intersections linear aggregates linearly independent Math matrix multiple neighbourhood Noether notation number of zeros obtain original surface period loops plane curve poles polynomial of grade polynomial vanishing positive integer prove Q places quantities quartic rational function regard result Riemann surface Riemann-Roch Theorem satisfied second kind second order sheets shew shewn suppose tangents Theory of Functions theta functions third kind transformation uniform function vanish identically variable Weierstrass's wherein