Abstract
For an abelian number field $K$, the discriminant can be obtained from the conductor~$m$ of~$K$, the degree of~$K$ over $\mathbb {Q}$, and the degrees of extensions $K\cdot \mathbb {Q}(\zeta _{m/p^{\alpha }})/\mathbb {Q}(\zeta _{m/p^{\alpha }})$, where $p$ runs through the set of primes that divide $m$, and $p^{\alpha }$ is the greatest power that divides~$m$. In this paper, we give a formula for computing the discriminant of any abelian number field.
Citation
Victor Bautista-Ancona. Jose Uc-Kuk. "The discriminant of abelian number fields." Rocky Mountain J. Math. 47 (1) 39 - 52, 2017. https://doi.org/10.1216/RMJ-2017-47-1-39
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