Algebraic independence by Mahler’s method and -unit equations
Very recently, the generating function of the Stern sequence , defined by and for any integer , has been considered from the arithmetical point of view. Coons [8] proved the transcendence of for every algebraic with , and this result was generalized in [6] to the effect that, for the same ’s, all numbers are algebraically independent. At about the same time, Bacher [4] studied the twisted version of Stern’s sequence, defined by and for any .The aim of our paper is to show...
Let be a power series , where is a strictly increasing linear recurrence sequence of non-negative integers, and a sequence of roots of unity in satisfying an appropriate technical condition. Then we are mainly interested in characterizing the algebraic independence over of the elements