β-expansion of unity and transcendence in the p-adic field

The aim of this paper is to study the ?-expansion of p-adic numbers. In particular, we obtain an upper bound of strings of consecutive zeros in the ?-expansion of unity for an algebraic number ? in Qp such that |?|p > 1.

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Publication Details

Journal
Filomat
Published
2025-01-01
DOI
https://doi.org/10.2298/fil2505709g
Primary Topic
advanced mathematical theories
Type
article
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article

β-expansion of unity and transcendence in the p-adic field

M. Ghorbel
Filomat
advanced mathematical theories
article

β-expansion of unity and transcendence in the p-adic field

M. Ghorbel
article en

Abstract

The aim of this paper is to study the ?-expansion of p-adic numbers. In particular, we obtain an upper bound of strings of consecutive zeros in the ?-expansion of unity for an algebraic number ? in Qp such that |?|p > 1.

FilomatVol. 39(5)
University of Sfax (TN)
Openalex Percentile: Top 75%
advanced mathematical theories
DOIOpen Access PDFOpenAlex
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