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arXiv · 1910.12148

On the moments of a polynomial in one variable

Michael Müger·Lars Tuset
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Abstract

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 $n\in{\mathbb N}$.

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Michael Müger, Lars Tuset. 2019-10-26. On the moments of a polynomial in one variable. https://doi.org/10.1016/j.indag.2019.11.003

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