Rendiconti del Seminario Matematico della Università di Padova


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Volume 126, 2011, pp. 63–72
DOI: 10.4171/RSMUP/126-4

Published online: 2011-12-31

Root Separation for Reducible Monic Quartics

Andrej Dujella[1] and Tomislav Pejkovič[2]

(1) University of Zagreb, Croatia
(2) University of Zagreb, Croatia

We study root separation for reducible monic integer polynomials of degree four. If $\text{H}(P)$ is the height and $\text{sep}(P)$ the minimal distance between two distinct roots of a separable integer polynomial $P(x)$, and $\text{sep}(P)=\text{H}(P)^{-e(P)}$, we show that $\limsup e(P)=2$, where limsup is taken over all reducible monic integer polynomials $P(x)$ of degree $4$.

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Dujella Andrej, Pejkovič Tomislav: Root Separation for Reducible Monic Quartics. Rend. Sem. Mat. Univ. Padova 126 (2011), 63-72. doi: 10.4171/RSMUP/126-4