Transcendence results on the generating functions of the characteristic functions of certain self-generating sets

摘要

1. Introduction and results. Quite recently, Dilcher and Stolarsky [11, Definition 5.1], introduced the two power series holomorphic on D:= {z ∈ C: |z| < 1}, and proved several functional equations relating them. Here the sequences of integers appearing in the exponents are examples of so-called self-generating sequences. In fact, if Ф and Г are minimal sets of non-negative integers such that 0 ∈ Φ ∩ Г and then Φ,Г are the sets of exponents of F, G, respectively. For properties of similarly defined sequences, see [4], for instance.