Congruences for the class numbers of real cyclic sextic number fields  

作　　者：刘通 

出　　处：《Science China Mathematics》1999年第10期1009-1018,共10页中国科学：数学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Grant No. 19771052).

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 K₆ be a real cyclic sextic number field, and K₂, K₃ its quadratic and cubic subfield. Let h（L） denote the ideal class number of field L. Seven congruences for h^- = h（K₆）/（h（K₂）h（K₃）） are obtained. In particular, when the conductor f₆ of K₆ is a prime p, （mod p）, where C is an explicitly given constant, and B_n is the Bernoulli number. These results on real cyclic sextic fields are an extension of the results on quadratic and cyclic quartic fields.

关 键 词：REAL CYCLIC sextic NUMBER field class NUMBER P-ADIC L-function. 

分 类 号：O156[理学—数学]