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ON TRANSCENDENTAL CONTINUED FRACTIONS IN FIELDS OF FORMAL POWER SERIES OVER FINITE FIELDS

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  01 October 2021

BÜŞRA CAN Open the ORCID record for BÜŞRA CAN [Opens in a new window]  and
GÜLCAN KEKEÇ Open the ORCID record for GÜLCAN KEKEÇ [Opens in a new window]
BÜŞRA CAN*
Affiliation:
Institute of Graduate Studies in Sciences, Istanbul University, Esnaf Hospital Building, 4th floor, Süleymaniye, Istanbul, Turkey and Department of Maritime Business Management, Faculty of Economics and Administrative Sciences, Piri Reis University, Postane District, Eflatun Street, No. 8, Tuzla 34940, Istanbul, Turkey e-mail: bcan@pirireis.edu.tr
GÜLCAN KEKEÇ
Affiliation:
Department of Mathematics, Faculty of Science, Istanbul University, 34134 Vezneciler, Istanbul, Turkey e-mail: gulkekec@istanbul.edu.tr
*
e-mail: busra.can.2018@ogr.iu.edu.tr
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Abstract

In the field of formal power series over a finite field, we prove a result which enables us to construct explicit examples of $U_{m}$-numbers by using continued fraction expansions of algebraic formal power series of degree $m>1$.

Keywords

Mahler’s classification of transcendental formal power series over a finite fieldU-numbercontinued fractiontranscendence measure

MSC classification

Primary: 11J61: Approximation in non-Archimedean valuations
Secondary: 11J70: Continued fractions and generalizations 11J82: Measures of irrationality and of transcendence

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 105 , Issue 3 , June 2022 , pp. 392 - 403
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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