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$U$-NUMBERS IN FIELDS OF FORMAL POWER SERIES OVER FINITE FIELDS

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  29 July 2019

GÜLCAN KEKEÇ Open the ORCID record for GÜLCAN KEKEÇ [Opens in a new window]
GÜLCAN KEKEÇ*
Affiliation:
Department of Mathematics, Faculty of Science, Istanbul University, 34134, Vezneciler, Istanbul, Turkey email gulkekec@istanbul.edu.tr
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Abstract

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In the field $\mathbb{K}$ of formal power series over a finite field $K$, we consider some lacunary power series with algebraic coefficients in a finite extension of $K(x)$. We show that the values of these series at nonzero algebraic arguments in $\mathbb{K}$ are $U$-numbers.

Keywords

Bundschuh’s classification of transcendental formal power series over finite fieldsU-numberlacunary power seriestranscendence measure

MSC classification

Primary: 11J61: Approximation in non-Archimedean valuations
Secondary: 11J82: Measures of irrationality and of transcendence
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 101 , Issue 2 , April 2020 , pp. 218 - 225
Copyright
© 2019 Australian Mathematical Publishing Association Inc.

References

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