Perucca, Antonella[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]

Sgobba, Pietro[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]

Tronto, Sebastiano[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]

Undated

No

[en] Kummer theory ; Kummer extension ; number field ; cyclotomic field ; quadratic field ; degree

[en] Let K be a quadratic number field. If \alpha \in K*, we describe an explicit procedure to compute all Kummer degrees [K(\zeta_m,\sqrt[n]{\alpha}):K(\zeta_m)] for n,m \geq 1, where \zeta_m denotes a primitive m-th root of unity and n divides m. We can also replace \alpha by any finitely generated subgroup of K*.