A property of algebraic univoque numbers

Abstract

Consider the set $\uu$ of real numbers $q\ge 1$ for which only one sequence $(c_i)$ of integers $0\le c_i\le q$ satisfies the equality ${\sum }_{i=1}^{\infty }{c}_i{q}^{-i}=1$. In this note we show that the set of algebraic numbers in $\uu$ is dense in the closure $\uuu$ of $\uu$.

5 pages, journal version, to appear in Acta Math. Hungar