On the irrationality exponent of the generating function for a class of integer sequences

Abstract

We derive the upper bound of the irrationality exponent for a class of integer sequences with an assumption on their generating functions. If their Hankel determinants are weakly non-vanishing, then we prove that (2logb−2log|a|)/(logb−2log|a|)is an upper bound of the irrationality exponent, where a∈Z/{0}and b∈Nsatisfying gcd(a,b)=1and b > a2. On the other hand, by the classical technique from Diophantine approximation and the structure of generating function, we achieve an upper bound of the irrationality exponent for the 3-fold Morse sequence, whose Hankel determinants are not well studied.