Monogenic polynomials having squarefull discriminant
Volume 222 / 2026
Acta Arithmetica 222 (2026), 99-106
MSC: Primary 11R04; Secondary 11R29, 11Y40
DOI: 10.4064/aa250117-22-2
Published online: 5 December 2025
Abstract
Given an integer $n \geq 2$, we produce infinitely many new families of monogenic polynomials $f(x)= x^{n-km} (x^k+A)^m+B \in \mathbb Z[x]$ having a powerful and $k$-full discriminant. Further, under certain assumptions, we give the asymptotics for the number of such monogenic polynomials with $B \leq X$.
