摘要
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.
Let K<sub>6</sub> be a real cyclic sextic number field, and K<sub>2</sub>, K<sub>3</sub> its quadratic and cubic subfield. Let h（L） denote the ideal class number of field L. Seven congruences for h<sup>-</sup> = h（K<sub>6</sub>）/（h（K<sub>2</sub>）h（K<sub>3</sub>）） are obtained. In particular, when the conductor f<sub>6</sub> of K<sub>6</sub> is a prime p, （mod p）, where C is an explicitly given constant, and B<sub>n</sub> is the Bernoulli number. These results on real cyclic sextic fields are an extension of the results on quadratic and cyclic quartic fields.
基金
Project supported by the National Natural Science Foundation of China (Grant No. 19771052).
