The probability that a random monic p-adic polynomial splits into linear factors

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70712Let n be a positive integer and let p be a prime. We calculate the probability that a random monic polynomial of degree n with coefficients in the ring Z_p of p-adic integers splits over Z_p into linear factors.24+2 pages, incl. 2 figures. Submitted to Experimental MathematicsNumber Theory11S05The probability that a random monic p-adic polynomial splits into linear factorstext