Rendiconti del Seminario Matematico della Università di Padova


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

Root Separation for Reducible Monic Quartics

Andrej Dujella[1] and Tomislav Pejkovič[2]

(1) Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000, Zagreb, Croatia
(2) Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000, 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