Transcendence of numbers with a low complexity expansion

[摘要] A sequence is Sturmian if it has complexity n + l - 1, that is, n + l - 1 factors of length n for every n; we show that real numbers whose expansion in some base k greater than or equal to I is Sturmian are transcendental, and give explicit expressions for these numbers. We then generalize the transcendence property to other sequences of low complexity, particularly the Arnoux-Rauzy sequences. (C) 1997 Academic Press.

[发布日期] 1997-12-01