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Speaker:
De-Jun Feng
Zugehörigkeit:
The Chinese University of Hong Kong
Datum:
Mon, 02/07/2018 - 15:00 - 15:50
Location:
MPIM Lecture Hall Let $q>1$ be a real number and $m\geq 1$ an integer. Let $Y$ denote the set of number $f(q)$ where $f$ runs over the integer polynomials with height not exceeding $m$. In this talk, we consider an old question when $Y$ is dense in the real line. This question is closely related to the studies of Bernoulli convolutions, beta-expansions and iterated functions systems. We prove the following conjecture of Erd\H{o}s et al.: $Y$ is dense if and only if $q$ is less than $m+1$ and is non-Pisot.
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