An Irrationality Measure for Regular Paperfolding Numbers
Michael James Coons, Paul Vrbik · 2012
Let F(z) = ∑ n�1 fnzn 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)) � 275331112987 = 2.002075359 · · · 137522851840 for all integers b � 2. This improves upon the previous bound of µ(F(1/b)) � 5 given by Adamczewski and Rivoal.