Theory Of The Algebraic Functions Of A Complex Variable

Author : John Charles Fields
Publisher : Forgotten Books
ISBN 13 : 9781330185988
Total Pages : 206 pages
Book Rating : 4.1/5 (859 download)

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Download or read book Theory of the Algebraic Functions of a Complex Variable written by John Charles Fields and published by Forgotten Books. This book was released on 2015-06-25 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Excerpt from Theory of the Algebraic Functions of a Complex Variable The theory of the algebraic functions developed in the following pages is algebraic in its methods and perfectly general. It holds for any algebraic equation reducible or irreducible, however complicated its singularities may be and whatever its character at infinity. The development of the theory may be said to culminate in the complementary theorem, in Chapter XII, from which theorem a number of well-known theorems in the theory of the algebraic functions immediately follow as corollaries. The principles here presented have been in the possession of the writer for some eight years past and had in fact, in a somewhat different form, already been written up with a view to publication in the summer of 1898. Other matters however intervened and the work was laid aside for a long period. Since then further interruptions have occurred, - the theory however has been twice rewritten in the interval and has probably lost nothing by the delay in publication. The writer has not felt it to be necessary to go into the theory of the Abelian integrals, his object having been attained on presenting the purely algebraic side of his subject. The principle embodied in the statement of the limitation on the orders of coincidence which a reduced form can have simultaneously with then branches of the fundamental algebraic equation, is evidently of wider scope than the theory of the algebraic functions. Also the method of the deformation of a product, or its equivalent, should find its application elsewhere, for example in the theory of the algebraic numbers and in the theory of the algebraic functions of several variables. In the latter connection the writer might say that he possesses a simple representation of the branches of an algebraic function of any number of variables in the neighborhood of a singular manifold and hopes to be able to utilize this representation in combination with the methods employed in the present volume. In conclusion the writer desires to express his thanks to Professor Mittag-Leffler and Professor Phragmén for the interest they have taken in his work. Acknowledgement is also due to the publishers, Messrs Mayer and Muller, for the obliging readiness with which they have always met the wishes of the author. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.