PURELY PERIODIC beta-EXPANSIONS IN CUBIC SALEM BASE IN F-q((X-1))

被引：0

作者：

Mahjoub, Faiza ^{[1
]}

机构：

[1] Univ Monastir, Dept Math, Higher Inst Appl Sci & Technol, Mahdia, Tunisia

来源：

PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD | 2016年 / 100卷 / 114期

关键词：

formal power series; finite fields; beta-expansion; Salem element;

D O I：

10.2298/PIM1614279M

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let F-q be the finite field with q elements and beta Salem series in F-q ((X-1)). It is proved in [15] that, in this case, all elements in F-q (X, beta) have purely periodic beta-expansion. We characterize the formal power series f in F-q (X, beta) with purely periodic beta-expansions by the conjugate vector (f) over tilde when beta is a cubic unit. No similar results exist in the real case.

引用

页码：279 / 285

页数：7

共 14 条

[1] Purely periodic beta-expansions with Pisot or Salem unit series in Fq((x-1))
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RESEARCH IN NUMBER THEORY, 2025, 11 (01)
[2] Purely periodic β-expansions with Pisot or Salem unit base in Fq ((X-1))
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[4] PURELY PERIODIC BETA-EXPANSIONS OVER LAURENT SERIES
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[8] Arithmetics of β- expansions in F q (( x-1 ))
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FILOMAT, 2024, 38 (25) : 8961 - 8970
[9] Purely periodic beta-expansions with Pisot or Salem unit series in Fq((x-1))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {F} _{q}((x^{-1}))$$\end{document}
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[10] Beta-expansion in Pisot and Salem unit bases in Fq((x-1))
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