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

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  07 June 2021

JASON BELL Open the ORCID record for JASON BELL [Opens in a new window]  and
YANN BUGEAUD Open the ORCID record for YANN BUGEAUD [Opens in a new window]
JASON BELL
Affiliation:
Department of Pure Mathematics University of WaterlooWaterloo, ONN2L 3G1Canadajpbell@uwaterloo.ca
YANN BUGEAUD*
Affiliation:
Université de Strasbourg Département de mathématiques 7, rue René Descartes, 67084StrasbourgFrance
*
bugeaud@math.unistra.fr
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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.

Keywords

Diophantine approximationpower series fieldMahler’s classification

MSC classification

Primary: 11J61: Approximation in non-Archimedean valuations
Secondary: 11J04: Homogeneous approximation to one number 11J81: Transcendence (general theory)
Type
Article
Information
Nagoya Mathematical Journal , Volume 246 , June 2022 , pp. 355 - 371
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Copyright
© (2021) The Authors. The publishing rights in this article are licenced to Foundation Nagoya Mathematical Journal under an exclusive license

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