The Diophantine Exponent of Algebraic Numbers for β-Expansions with a Negative Base
Authors
Osama A. B. Shafah
Department of Mathematical Sciences, Libyan Academy for Postgraduate Studies, Tripoli, Libya. (LY)
Mohamed Hbaib
Department of Mathematics, Faculty of Science in Sfax, Bp. 802,3038 Sfax, Tunisia. (LY)
Asmaa Omar Mubayrash
Department of Mathematics., Faculty of Science, Subratah University, Libya. (LY)
Article Information
DOI: 10.51583/IJLTEMAS.2025.1409000009
Subject Category: Algebra
Volume/Issue: 14/9 | Page No: 66-71
Publication Timeline
Submitted: 2025-09-27
Published: 2025-09-27
Abstract
Abstract: The aim of this paper is to prove that the Diophantine exponent is bounded by , where is an algebraic number, and is the Mahler measure of . In addition, a new result will be founded about transcendental number when is infinite.
Keywords
β-Expansion, Diophantine Approx- imation, Transcendental, Mahler Measure, Negative Base
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References
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