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MAHLER’S AND KOKSMA’S CLASSIFICATIONS IN FIELDS OF POWER SERIES

Published online by Cambridge University Press:  07 June 2021

JASON BELL
Affiliation:
Department of Pure Mathematics University of Waterloo Waterloo, ON N2L 3G1 Canada jpbell@uwaterloo.ca
YANN BUGEAUD
Affiliation:
Université de Strasbourg Département de mathématiques 7, rue René Descartes, 67084 Strasbourg France
Corresponding

Abstract

Let q a prime power and ${\mathbb F}_q$ the finite field of q elements. We study the analogues of Mahler’s and Koksma’s classifications of complex numbers for power series in ${\mathbb F}_q((T^{-1}))$. Among other results, we establish that both classifications coincide, thereby answering a question of Ooto.

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(2021) The Authors. The publishing rights in this article are licenced to Foundation Nagoya Mathematical Journal under an exclusive license

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MAHLER’S AND KOKSMA’S CLASSIFICATIONS IN FIELDS OF POWER SERIES
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