Root separation for polynomials with reducible derivative

Year, pages: 2020, 1079 - 1086

Suppose $f$ is a degree $d$ polynomial with integer coefficients whose derivative $f'$ is a polynomial reducible over $\Q$. We give a lower bound for the distance between two distinct roots of $f$ in terms of $d$, the height $H(f)$ of $f$, and the degree $m$ of the irreducible factor of $f'$ with largest degree. The exponent $(d+m-1)/2$ that appears as the power of $H(f)$ is smaller than the corresponding exponent $d-1$ in Mahler's bound.

Dubickas, A. 2020. Root separation for polynomials with reducible derivative. In Mathematica Slovaca, vol. 70, no.5, pp. 1079-1086. 0139-9918. DOI: https://doi.org/ 10.1515/ms-2017-0415

Dubickas, A. (2020). Root separation for polynomials with reducible derivative. Mathematica Slovaca, 70(5), 1079-1086. 0139-9918. DOI: https://doi.org/ 10.1515/ms-2017-0415

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava