  Let $f$ be a non-zero polynomial with complex coefficients and define
$M_n(f)=\int_0^1f(x)^n\,dx$. We use ideas of Duistermaat and van der Kallen to
prove $\limsup_{n\rightarrow\infty}|M_n(f)|^{1/n}>0$. In particular, $M_n(f)\ne
0$ for infinitely many $n\in{\mathbb N}$.

Complex Variables