Periodic expansion of one by Salem numbers

2022/06/14 by Akiyama, Shigeki, Hichri, Hachem
#11K16 #37B10 #37E05 #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2206.06675

Abstract

We show that for a Salem number β of degree d, there exists a positive constant c(d) that β^m is a Parry number for integers m of natural density ≥ c(d). Further, we show c(6)>1/2 and discuss a relation to the discretized rotation in dimension 4.

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