Stern polynomials and algebraic independence

Abstract

Let $t\ge 2$ and $k\ge 1$ be integers. Let $H_k(z)$ with $\left|z\right|<1$ be the limit of a certain subsequence of the Stern polynomials introduced by Dilcher and Eriksen. We use Mahler's method to prove the algebraic independence of the values at nonzero algebraic points of the functions $H_k(z)$ and $H_k(z^{t^k})$.

7 pages