On the distribution of reducible polynomials

2020/08/13 by Kuba, Gerald · 3 citations
#FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2008.05815

Abstract

Let Y_n(t) denote the set of all polynomials over the ring Z which are reducible over the field Q and of degree n>1 and of height not greater than t. We show that the true order of magnitude of |Y_n(t)| equals t² log t in the special case n=2 and it equals tⁿ for each n>2. We also determine the true order of magnitude of the size of certain interesting subsets of Y_n(t).

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