Infinite products related to generalized Thue-Morse sequences

Abstract

Given an integer q ≥ 2 and θ 1 , • • • , θ q−1 ∈ {0, 1}, let (θ n ) n≥0 be the generalized Thue-Morse sequence, defined to be the unique fixed point of the morphismbeginning with θ 0 := 0, where 0 := 1 and 1 := 0. For rational functions R, we study infinite products of the forms