On the conjecture of Erdos, Joo and Komornik for p-adic numbers

被引：0
|
作者：
Hbaib, M. [1 ]
Guidara, S. [1 ]
Zouari, S. [1 ]
机构：
[1] Univ Sfax, Fac Sci, BP 1171, Sfax 3000, Tunisia
来源：
RESEARCH IN NUMBER THEORY | 2024年 / 10卷 / 03期
关键词：
p-adic number; beta-expansion; Pisot-Chabauty number; PISOT; APPROXIMATION; POLYNOMIALS; PROPERTY; SPECTRA;
D O I：
10.1007/s40993-024-00558-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
he aim of this study is to give a partial answer to the analogue conjecture of Erd & odblac;s, Jo & ograve; and Komornik in the field of p-adic numbers. We prove that if beta is a Pisot-Chabauty p-adic number, then the quantity lm(beta) is strictly positive where l(m)(beta)=inf{|x|(p):x is an element of Lambda(m)(beta)-Lambda(m)(beta),x not equal 0} and Lambda(m)(beta)={& sum;(n)(i=0)a(i)beta(i) :ai is an element of Z[1/p]boolean AND[0,1[ , |a(i)|p <= p(m)}.
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