Many mathematicians have investigated the base- expansions for integral base-, and more general -expansions for a real number . However, little is known on the -expansions of algebraic numbers. The main purpose of this paper is to give new lower bounds for the numbers of nonzero digits in the -expansions of algebraic numbers under the assumption that is a Pisot or Salem number. As a consequence of our main results, we study the arithmetical properties of power series , where is a real number and .
Cite this article
Hajme Kaneko, On the number of nonzero digits in the beta-expansions of algebraic numbers. Rend. Sem. Mat. Univ. Padova 136 (2016), pp. 205–223DOI 10.4171/RSMUP/136-14