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

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)}.