I'm looking for a monograph (book, article, lecture notes, whatever) about the representation of numbers (real or complex) in non-integer bases.
I am especially interested in results about algebraic numbers. For example, possible equivalent conditions to "a real number in $[0,1)$ has a periodic $\beta$-expansion iff it lies in $\Bbb{Q}(\beta)$".
All I could find on my own were the relevant Wikipedia page and lots of results on the uniqueness of $\beta$ expansions of almost every number (for appropriate $\beta$, wrt an appropriate measure).