Mathematical Journal of Ibaraki University
Online ISSN : 1883-4353
Print ISSN : 1343-3636
ISSN-L : 1343-3636
Note on class number parity of an abelian field of prime conductor, III
Humio Ichimura
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2019 Volume 51 Pages 39-48

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Abstract

Let p be a prime number of the form p = 2+1 with some odd prime number . For such a prime number p, it is shown that the relative class number hp- of the pth cyclotomic field Q(ζp) is odd when 2 remains prime in Q(ζ)+ by Estes [3], Stevenhagen [11] and Metsänkylä [8] using a Bernoulli number associated to Q(ζp). In this note, we give an alternative proof of the assertion using a cyclotomic unit of Q(ζp)+.

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© 2019 Department of Mathematics, Faculty of Science, Ibaraki University
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