eBook ISBN:  9781470431655 
Product Code:  COLL/16.E 
List Price:  $60.00 
MAA Member Price:  $54.00 
AMS Member Price:  $48.00 
eBook ISBN:  9781470431655 
Product Code:  COLL/16.E 
List Price:  $60.00 
MAA Member Price:  $54.00 
AMS Member Price:  $48.00 

Book DetailsColloquium PublicationsVolume: 16; 1933; 218 ppMSC: Primary 14
This book, immediately striking for its conciseness, is one of the most remarkable works ever produced on the subject of algebraic functions and their integrals. The distinguishing feature of the book is its third chapter, on rational functions, which gives an extremely brief and clear account of the theory of divisors....
A very readable account is given of the topology of Riemann surfaces and of the general properties of abelian integrals. Abel's theorem is presented, with some simple applications. The inversion problem is studied for the cases of genus zero and genus unity. The chapter on the reduction of singularities is very noteworthy.... A final chapter illustrates the general theory with some examples. In particular, constructive methods are given for treating algebraic relations which are of the third degree in one of the variables.... The arithmetic theory of algebraic functions is a good thing. In making its study easy, Bliss has performed a service which will win him the gratitude of an ever increasing number of readers.
—Bulletin of the American Mathematical Society
ReadershipGraduate students and research mathematicians interested in algebraic functions and their integrals.

Table of Contents

Chapters

Chapter I. Singlevalued analytic functions

Chapter II. Algebraic functions and their expansions

Chapter III. Rational functions

Chapter IV. The Riemann surface of an algebraic function

Chapter V. Integrals of rational functions

Chapter VI. Abel’s theorem

Chapter VII. Birational transformations

Chapter VIII. The reduction of singularities by transformation

Chapter IX. Inversion of Abelian integrals

Chapter X. Examples


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This book, immediately striking for its conciseness, is one of the most remarkable works ever produced on the subject of algebraic functions and their integrals. The distinguishing feature of the book is its third chapter, on rational functions, which gives an extremely brief and clear account of the theory of divisors....
A very readable account is given of the topology of Riemann surfaces and of the general properties of abelian integrals. Abel's theorem is presented, with some simple applications. The inversion problem is studied for the cases of genus zero and genus unity. The chapter on the reduction of singularities is very noteworthy.... A final chapter illustrates the general theory with some examples. In particular, constructive methods are given for treating algebraic relations which are of the third degree in one of the variables.... The arithmetic theory of algebraic functions is a good thing. In making its study easy, Bliss has performed a service which will win him the gratitude of an ever increasing number of readers.
—Bulletin of the American Mathematical Society
Graduate students and research mathematicians interested in algebraic functions and their integrals.

Chapters

Chapter I. Singlevalued analytic functions

Chapter II. Algebraic functions and their expansions

Chapter III. Rational functions

Chapter IV. The Riemann surface of an algebraic function

Chapter V. Integrals of rational functions

Chapter VI. Abel’s theorem

Chapter VII. Birational transformations

Chapter VIII. The reduction of singularities by transformation

Chapter IX. Inversion of Abelian integrals

Chapter X. Examples