Rad HAZU, Matematičke znanosti, Vol. 20 (2016), 9-18.

P-ADIC ROOT SEPARATION FOR QUADRATIC AND CUBIC POLYNOMIALS

Tomislav Pejković

Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia
e-mail: pejkovic@math.hr


Abstract.   We study p-adic root separation for quadratic and cubic polynomials with integer coefficients. The quadratic and reducible cubic polynomials are completely understood, while in the irreducible cubic case and p ≠ 2, we give a family of polynomials with the bound which is the best currently known.

2010 Mathematics Subject Classification.   11C08, 11B37, 11J61.

Key words and phrases.   Integer polynomials, root separation, p-adic numbers.


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