On the reduced length of a polynomial with real coefficients

Abstract

The length $L(P)$ of a polynomial $P$ is the sum of the absolute values of the coefficients. For $P\in\mathbb{R}[x]$ the properties of $l(P)$ are studied, where $l(P)$ is the infimum of $L(PG)$ for $G$ running through monic polynomials over $\mathbb{R}$.