The degree of Kummer extensions of number fields – Flavio Perissinotto (University of Luxembourg)

Aula Seminari

Abstract

Under the Generalized Riemann Hypothesis, densities of prime ideals of a number field $K$ for which a given subgroup $G$ of $K^\times$ has a certain cardinality modulo those primes can be computed, and their formulas involve degrees of torsion-Kummer extensions of such a number field, namely degrees $[K(\zeta_N, \sqrt[M]{G}):K]$ for $M|N$. In this talk, we will see strategies to explicitly compute such degrees and to compute them for all M and N at once with a finite procedure. We will focus on Kummer extensions of multiquadratic and quartic cyclic number fields.

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