Abstract: For an abelian number field K, the discriminant can be obtained from the conductor m of K, the degree of K over and the degrees of extensions where p runs through the set of primes that divide m, and is the greatest power that divides m. In this paper, we give some results about the relation of the parity of the conductor with the sign of the discriminant. Further, we give some expressions to calculate the discriminant of an abelian number field, which depend only on the degree of such a field and its uniqueness also due to the degree. |
Keywords and phrases: cyclotomic fields, abelian number fields, conductors, discriminant.
Received: December 22, 2020; Accepted: January 9, 2021; Published: February 22, 2021
How to cite this article: Victor Bautista-Ancona and Jose Uc-Kuk, Some results about the discriminant of Abelian number fields, JP Journal of Algebra, Number Theory and Applications 49(2) (2021), 101-120. DOI: 10.17654/NT049010101
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
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