Abelian Functions: Abel's Theorem and the Allied Theory of Theta Functions (Cambridge Mathematical Library) (Paperback)

by H. F. Baker (Author), Igor Krichever (Foreword) "THIS book is concerned with a particular development of the theory of the algebraic irrationally arising when a quantity y is defined in terms of..." (more)
Key Phrases: Acta Math, Collected Works, Abel'schen Functionen (more...)

Editorial Reviews

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

Product Description
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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Product Details

• Paperback: 724 pages
• Publisher: Cambridge University Press (February 23, 1996)
• Language: English
• ISBN-10: 0521498775
• ISBN-13: 978-0521498777
• Product Dimensions: 9.2 x 5.7 x 1.6 inches
• Shipping Weight: 2.2 pounds (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars See all reviews (1 customer review)
• Amazon.com Sales Rank: #2,135,979 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

8 of 8 people found the following review helpful:

5.0 out of 5 stars A precious jewel !, May 11, 2001

By	Leonidas S. Junior (São Paulo, Brasil) - See all my reviews (REAL NAME)

When I was a Ph.D. student and had some problems finding suitable functions in order to study the multiloop scattering of strings, I found this rarity of a book. Although it was first published a long time ago (1897) it is probably one of the most complete works on complex functions of many variables and particularly on theta functions of many variables. In this book you can find some material that is not in any other book I know of, and the style makes it relatively easy to read.

It covers a large number of subjects, like Abel's theorem, abelian integrals of the first and second type, Riemann's theta functions, hyperelliptic (many variables) theta functions, radical and factorial functions, Jacobian functions, and degenerate abelian integrals.

I consider it a jewel among the books that cover the same subject, both for its completenes and its writing style.