Irrationality measures for some automatic real numbers
نویسندگان
چکیده
منابع مشابه
Irrationality measures for some automatic real numbers
This paper is devoted to the rational approximation of automatic real numbers, that is, real numbers whose expansion in an integer base can be generated by a finite automaton. We derive upper bounds for the irrationality exponent of famous automatic real numbers associated with the Thue–Morse, Rudin–Shapiro, paperfolding and Baum–Sweet sequences. These upper bounds arise from the construction o...
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This paper addresses the problem of determining the best results one can expect using the Thue-Siegel method as developed by Bombieri in his equivariant approach to effective irrationality measures to roots of high order of algebraic numbers, in the non-archimedean setting. As an application, we show that this method, under a nonvanishing assumption for the auxiliary polynomial which replaces t...
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Let F(z) = ∑ n>1 fnz n be the generating series of the regular paperfolding sequence. For a real number α the irrationality exponent μ(α), of α, is defined as the supremum of the set of real numbers μ such that the inequality |α − p/q| < q−μ has infinitely many solutions (p, q) ∈ Z × N. In this paper, using a method introduced by Bugeaud, we prove that μ(F(1/b)) 6 275331112987 137522851840 = 2....
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ژورنال
عنوان ژورنال: Mathematical Proceedings of the Cambridge Philosophical Society
سال: 2009
ISSN: 0305-0041,1469-8064
DOI: 10.1017/s0305004109002643