On Computing Discriminants of Subfields of Q(ζpr)

✍ Scribed by Trajano Pires da Nóbrega Neto; J.Carmelo Interlando; José Othon Dantas Lopes

• Book ID: 102601668
• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 105 KB
• Volume: 96
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1006/jnth.2002.2796

✦ Synopsis

The conductor-discriminant formula, namely, the Hasse Theorem, states that if a number field K is fixed by a subgroup H of GalðQðz n Þ=QÞ; the discriminant of K can be obtained from H by computing the product of the conductors of all characters defined modulo n which are associated to K: By calculating these conductors explicitly, we derive a formula to compute the discriminant of any subfield of Qðz p r Þ; where p is an odd prime and r is a positive integer.