Some new infinite families of monogenic polynomials with non-squarefree discriminant
Volume 197 / 2021
Acta Arithmetica 197 (2021), 213-219 MSC: Primary 11R04; Secondary 11R09, 12F05. DOI: 10.4064/aa200211-21-7 Published online: 12 October 2020
In previous work, a method of Kedlaya was modified to construct explicit infinite families of monogenic polynomials of degree $p$, for any prime $p\ge 3$, having non-squarefree discriminant. In this article, we use a different approach, which allows us to remove the prime-degree restriction, to prove, for any $n\ge 4$, the existence of infinitely many monogenic polynomials of degree $n$ that have non-squarefree discriminant.