JournalsrsmupVol. 126pp. 63–72

Root Separation for Reducible Monic Quartics

  • Andrej Dujella

    University of Zagreb, Croatia
  • Tomislav Pejkovič

    University of Zagreb, Croatia
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Abstract

We study root separation for reducible monic integer polynomials of degree four. If H(P)\text{H}(P) is the height and sep(P)\text{sep}(P) the minimal distance between two distinct roots of a separable integer polynomial P(x)P(x), and sep(P)=H(P)e(P)\text{sep}(P)=\text{H}(P)^{-e(P)}, we show that lim supe(P)=2\limsup e(P)=2, where limsup is taken over all reducible monic integer polynomials P(x)P(x) of degree 44.

Cite this article

Andrej Dujella, Tomislav Pejkovič, Root Separation for Reducible Monic Quartics. Rend. Sem. Mat. Univ. Padova 126 (2011), pp. 63–72

DOI 10.4171/RSMUP/126-4