An Irrationality Measure for Regular Paperfolding Numbers

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 = 2.002075359 · · ·