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Congruences for the class numbers of real cyclic sextic number fields

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Abstract

LetK 6 be a real cyclic sextic number field, andK 2,K 3 its quadratic and cubic subfield. Leth(L) denote the ideal class number of fieldL. Seven congruences forh - =h (K 6)/(h(K 2)h(K 3)) are obtained. In particular, when the conductorf 6 ofK 6 is a primep,\(Ch^ - \equiv B\tfrac{{p - 1}}{6}B\tfrac{{5(p - 1)}}{6}(\bmod p)\), whereC is an explicitly given constant, andB n is the Bernoulli number. These results on real cyclic sextic fields are an extension of the results on quadratic and cyclic quartic fields.

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Authors and Affiliations

  1. Department of Applied Mathematics, Tsinghua University, 100084, Beijing, China

    Tong Liu

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  1. Tong Liu
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Project supported by the National Natural Science Foundation of China (Grant No. 19771052).

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Liu, T. Congruences for the class numbers of real cyclic sextic number fields. Sci. China Ser. A-Math. 42, 1009–1018 (1999). https://doi.org/10.1007/BF02889501

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  • DOI: https://doi.org/10.1007/BF02889501

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