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Diophantine Equations over Function Fields : London Mathematical Society Lecture Note Series - R. C. Mason

Diophantine Equations over Function Fields

London Mathematical Society Lecture Note Series

Paperback

Published: 25th June 1984
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Diophantine equations over number fields have formed one of the most important and fruitful areas of mathematics throughout civilisation. In recent years increasing interest has been aroused in the analogous area of equations over function fields. However, although considerable progress has been made by previous authors, none has attempted the central problem of providing methods for the actual solution of such equations. The latter is the purpose and achievement of this volume: algorithms are provided for the complete resolution of various families of equations, such as those of Thue, hyperelliptic and genus one type. The results are achieved by means of an original fundamental inequality, first announced by the author in 1982. Several specific examples are included as illustrations of the general method and as a testimony to its efficiency. Furthermore, bounds are obtained on the solutions which improve on those obtained previously by other means. Extending the equality to a different setting, namely that of positive characteristic, enables the various families of equations to be resolved in that circumstance. Finally, by applying the inequality in a different manner, simple bounds are determined on their solutions in rational functions of the general superelliptic equation. This book represents a self-contained account of a new approach to the subject, and one which plainly has not reached the full extent of its application. It also provides a more direct on the problems than any previous book. Little expert knowledge is required to follow the theory presented, and it will appeal to professional mathematicians, research students and the enthusiastic undergraduate.

Preface
The fundamental inequality
The Thue equation
The hyperelliptic equation
Equations of small genus
Bounds for equations of small genus
Fields of arbitrary characteristics
Solutions for non-zero characteristic
The superelliptic equation
References
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521269834
ISBN-10: 0521269830
Series: London Mathematical Society Lecture Note Series
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 136
Published: 25th June 1984
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 0.8
Weight (kg): 0.21