On the moments of a polynomial in one variable

Abstract

Let $f$ be a non-zero polynomial with complex coefficients and define $M_n(f)={\int }_0^{1}f(x{)}^{n}dx$. We use ideas of Duistermaat and van der Kallen to prove ${\mathrm{limsup}}_{n\to \infty }|M_n(f){|}^{1/n}>0$. In particular, $M_n(f)\ne 0$ for infinitely many $n\in \mathbb{N}$.

4 pages, no figures

Cited by in corpus (2)

• The Mathieu conjecture for $SU(2)$ reduced to an abelian conjecture
• An integral formula for Lie groups, and the Mathieu conjecture reduced to Abelian non-Lie conjectures