**Colloquium Publications**

Volume: 16;
1933;
218 pp;
Softcover

MSC: Primary 14;

**Print ISBN: 978-0-8218-4607-0
Product Code: COLL/16**

List Price: $60.00

AMS Member Price: $48.00

MAA Member Price: $54.00

**Electronic ISBN: 978-1-4704-3165-5
Product Code: COLL/16.E**

List Price: $56.00

AMS Member Price: $44.80

MAA Member Price: $50.40

# Algebraic Functions

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*Gilbert Ames Bliss*

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

#### Readership

Graduate students and research mathematicians interested in algebraic functions and their integrals.

#### Table of Contents

# Table of Contents

## Algebraic Functions

- Cover Cover11
- Title page i2
- Preface iii4
- Contents vii8
- Chapter I. Single-valued analytic functions 112
- Chapter II. Algebraic functions and their expansions 2435
- Chapter III. Rational functions 4354
- Chapter IV. The Riemann surface of an algebraic function 7586
- Chapter V. Integrals of rational functions 93104
- Chapter VI. Abel’s theorem 119130
- Chapter VII. Birational transformations 133144
- Chapter VIII. The reduction of singularities by transformation 155166
- Chapter IX. Inversion of Abelian integrals 169180
- Chapter X. Examples 183194
- List of references 214225
- Index 217228
- Back Cover Back Cover1230