On the beta-expansions of 1 and algebraic numbers for a Salem number beta

We study the digits of beta- expansions in the case where beta is a Salem number. We introduce new upper bounds for the numbers of occurrences of consecutive 0s in the expansion of 1. We also give lower bounds for the numbers of non-zero digits in the beta-expansions of algebraic numbers. As applications, we give criteria for transcendence of the values of power series at certain algebraic points.