Congruences for the class numbers of real cyclic sextic number fields (Q1974215)

Extending results on quadratic and cyclic quartic fields the author studies the class number \(h\) of real cyclic sextic number fields \(K\). Seven congruences are obtained. In particular when the conductor of \(K\) is a prime \(p\), then \[ C\cdot h^-\equiv B_{{p-1}\over{6}}\cdot B_{{5(p-1)}\over{6}} (\bmod p) \] where \(C\) is an explicitly given constant.