On some arithmetic properties of Mahler functions (Q1618140)

The paper is concerned with Mahler functions: power series \(f(x)\) with complex coefficients for which there exist a natural number \(n\) and an integer \(\ell \geq 2\) such that \(f(x)\), \(f(x^\ell),\ldots,f(x^{\ell^{n-1} }),f(x^{\ell^n})\) are linearly independent. The authors consider the special case where \(p(x)\) is a polynomial with integer coefficients and \(f(x)=p(x)f(x^\ell)\) and they consider the relationship between properties of the polynomials \(p,f\). They also give some general results on Mahler functions that relate to results on E-functions and G-functions.