On the discriminant of pure number fields

2020/05/04 by Jakhar, Anuj, Khanduja, Sudesh K., Sangwan, Neeraj
#11R04 #11R29 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2005.01300

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\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.

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