engleski

Root separation for reducible monic quartics

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

integer polynomials ; root separation

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