JournalsrmiVol. 28, No. 4pp. 931–946

On the expansions of a real number to several integer bases

  • Yann Bugeaud

    Université de Strasbourg, France
On the expansions of a real number  to several integer bases cover
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Abstract

Very little is known about the expansions of a real number in several integer bases. We establish various results showing that the expansions of a real number in two multiplicatively independent bases cannot both be simple, in a suitable sense. We also construct explicitly a real number ξ\xi which is rich to all integer bases, that is, with the property that, for every integer b2b \ge 2, every finite block of letters in the alphabet {0,1,,b1}\{0, 1, \dots , b-1\} occurs in the bb-ary expansion of ξ\xi.

Cite this article

Yann Bugeaud, On the expansions of a real number to several integer bases. Rev. Mat. Iberoam. 28 (2012), no. 4, pp. 931–946

DOI 10.4171/RMI/697