Algebraic independence of the values of Mahler functions associated with a certain continued fraction expansion

AbstractIt is proved that the function Θ(z)=∑k⩾0zR0+R1+⋯+Rk(1−zR0)(1−zR1)⋯(1−zRk), which can be expressed as a certain continued fraction, takes algebraically independent values at any distinct nonzero algebraic numbers inside the unit circle if the sequence {Rk}k⩾0 is the generalized Fibonacci numbers