Rocky Mountain Journal of Mathematics

The discriminant of abelian number fields

Victor Bautista-Ancona and Jose Uc-Kuk

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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.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 1 (2017), 39-52.

Dates
First available in Project Euclid: 3 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1488531893

Digital Object Identifier
doi:10.1216/RMJ-2017-47-1-39

Mathematical Reviews number (MathSciNet)
MR3619757

Zentralblatt MATH identifier
1362.11088

Subjects
Primary: 11R18: Cyclotomic extensions 11R29: Class numbers, class groups, discriminants

Keywords
Cyclotomic fields abelian number fields conductors discriminant

Citation

Bautista-Ancona, Victor; Uc-Kuk, Jose. The discriminant of abelian number fields. Rocky Mountain J. Math. 47 (2017), no. 1, 39--52. doi:10.1216/RMJ-2017-47-1-39. https://projecteuclid.org/euclid.rmjm/1488531893


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References

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