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ON THE DISCRIMINANT OF PURE NUMBER FIELDS
Journal
Colloquium Mathematicum
ISSN
00101354
Date Issued
2022-01-01
Author(s)
Jakhar, Anuj
Khanduja, Sudesh K.
Sangwan, Neeraj
Abstract
Let K = Q(n√a) be an extension of degree n of the field Q of rational numbers, where the integer a is such that for each prime p dividing n either p ∤ 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.
Subjects