Nombres algébriques et substitutions
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Publication:3672080
DOI10.24033/bsmf.1957zbMath0522.10032OpenAlexW194037683MaRDI QIDQ3672080
Publication date: 1982
Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)
Full work available at URL: http://www.numdam.org/item?id=BSMF_1982__110__147_0
Radix representation; digital problems (11A63) Distribution modulo one (11J71) General theory of distribution modulo (1) (11K06)
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Cites Work
