Mahler Functions and Transcendence

Kumiko Nishioka (auth.)9783540614722, 3-540-61472-9

This book is the first comprehensive treatise of the transcendence theory of Mahler functions and their values. Recently the theory has seen profound development and has found a diversity of applications. The book assumes a background in elementary field theory, p-adic field, algebraic function field of one variable and rudiments of ring theory. The book is intended for both graduate students and researchers who are interested in transcendence theory. It will lay the foundations of the theory of Mahler functions and provide a source of further research.

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Table of contents :
Transcendence theory of mahler functions of one variable….Pages 1-32
Transcendence theory of mahler functions of several variables….Pages 33-77
Algebraic independence of mahler functions and their values….Pages 78-117
Applications of elimination theory….Pages 118-149
Regular sequences and mahler functions….Pages 150-175