Bertrand-Mathis: Nombres normaux dans diverses bases

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Anne Bertrand-Mathis
Nombres normaux dans diverses bases
Annales de l'institut Fourier, 45 no. 5 (1995), p. 1205-1222, doi: 10.5802/aif.1492
Article PDF | Reviews MR 97m:11103 | Zbl 0833.11033 | 1 citation in Cedram

Résumé - Abstract

Following a paper of Feldman and Smorodinsky, we study occurrence of a fixed block of digits in the $\theta $-development of $\beta ^n$. We show that for non-equivalent Pisot numbers $\beta $ and $\theta $, the set of $\beta $-digit normal numbers and $\theta $-digit normal numbers are different; we also show that for two non equivalent algebraic integers $\beta $ and $\theta $ with $\theta $ Pisot, the set of geometric normal numbers in $\theta $-basis respectively are different.

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