On the number of unique expansions in non-integer bases |
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Authors: | Martijn de Vries |
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Affiliation: | Delft University of Technology, EEMCS Faculty, Mekelweg 4, 2628 CD Delft, The Netherlands |
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Abstract: | Let q>1 be a real number and let m=m(q) be the largest integer smaller than q. It is well known that each number can be written as with integer coefficients 0?ci<q. If q is a non-integer, then almost every x∈Jq has continuum many expansions of this form. In this note we consider some properties of the set Uq consisting of numbers x∈Jq having a unique representation of this form. More specifically, we compare the size of the sets Uq and Ur for values q and r satisfying 1<q<r and m(q)=m(r). |
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Keywords: | primary, 11A63 secondary, 11B83 |
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