Mathematical Journal of Ibaraki University
Online ISSN : 1883-4353
Print ISSN : 1343-3636
ISSN-L : 1343-3636
Indivisibility of the class number of a real abelian field of prime conductor
Shoichi FujimaHumio Ichimura
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2021 Volume 53 Pages 1-16

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Abstract

For a fixed integer n ≥ 1, let p = 2nℓ + 1 be a prime number with an odd prime number and let F = Fp,ℓ be the real abelian field of conductor p and degree . When n ≤ 21, we show that a prime number r does not divide the class number hF of F whenever r is a primitive root modulo with the help of computer. This generalizes a result of Jakubec and Metsänkylä for the case n = 1.

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© 2021 Department of Mathematics, Faculty of Science, Ibaraki University
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