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Congruences of Ankeny-Artin-Chowla type for pure quartic and sectic fields

Published online by Cambridge University Press:  22 January 2016

Masato Kamei
Masato Kamei*
Affiliation:
Department of Mathematics Faculty of Science, Kyoto University, Sakyō-ku, Kyoto 606, Japan
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Ankeny, Artin and Chowla [1] showed that there are congruences between class numbers of real quadratic fields and generalized Bernoulli numbers. Recently, Ito [3] has extended their results to the case of pure cubic fields using generalized Hurwitz numbers of Lichtenbaum [4]. In his paper, he suggested that similar results would be obtained for pure quartic and sectic fields. In this paper, we carry out this by following his idea. To give a congruence in an exact form, we need an idea due to Matthews [5]. As the argument in the sectic case is quite parallel to that in the quartic case, we shall discuss the former case briefly in the last two sections.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 108 , December 1987 , pp. 131 - 144
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1987

References

[ 1 ] Ankeny, N., Artin, E. and Chowla, S., The class number of real quadratic fields, Ann. of Math., (2), 56 (1952), 479–493.Google Scholar
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