Abstract
AbstractWe 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have