Transcendence of dendric beta-expansions with pure discrete spectrum
Jihyuk Seo, Wolfgang Steiner
Abstract
We prove the transcendence of numbers that have β-expansions in algebraic bases β belonging to dendric shifts with purely discrete spectrum, under certain combinatorial conditions on their directive sequences of substitutions. This includes Arnoux-Rauzy sequences on arbitrary alphabets and Cassaigne-Selmer sequences. The proof uses Rauzy fractals and the subspace theorem.
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