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Let be an algebraic number. We study the strings of zeros (“gaps”) in the Rényi -expansion of unity which controls the set of -integers. Using a version of Liouville’s inequality which extends Mahler’s and Güting’s approximation theorems, the strings of zeros in are shown to exhibit a “gappiness” asymptotically bounded above by , where is the Mahler measure of . The proof of this result provides in a natural way a new classification of algebraic numbers with classes called Q...
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