Transcendence of dendric beta-expansions with pure discrete spectrum
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.
math.NT↗