For an abelian number field K, the discriminant can be obtained from the conductor m of K, the degree of K over Q, and the degrees of extensions, where p runs through the set of primes that divide m, and p α is the greatest power that divides m. In this paper, we give a formula for computing the discriminant of any abelian number field. 2010 AMS Mathematics subject classification. Primary 11R18, 11R29. Keywords and phrases. Cyclotomic fields, abelian number fields, conductors, discriminant.The second author was supported by Consejo Nacional de Ciencia y Tecnología (CONACyT).

No abstract