On the discriminant of pure number fields
Tom 167 / 2022
Colloquium Mathematicum 167 (2022), 149-157
MSC: 11R04, 11R29.
DOI: 10.4064/cm8257-11-2020
Opublikowany online: 24 May 2021
Streszczenie
Let be an extension of degree n of the field \mathbb Q of rational numbers, where the integer a is such that for each prime p dividing n either p\nmid a or the highest power of p dividing a is coprime to p; this condition is clearly satisfied when a, n are coprime or a is squarefree. The paper contains an explicit formula for the discriminant of K involving only the prime powers dividing a,n.
