Dedekind zeta-functions and Dedekind sums  

作　　者：陆洪文 焦荣政 纪春岗 

出　　处：《Science China Mathematics》2002年第8期1059-1065,共7页中国科学：数学（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China (Grant No. 10171076).

摘　　要：In this paper we use Dedekind zeta functions of two real quadratic number fields at -1 to denote Dedekind sums of high rank. Our formula is different from that of Siegel’s. As an application, we get a polynomial representation of ζK(-1): ζK(-1) = 1/45(26n3 -41n± 9),n = ±2(mod 5), where K = Q(√5q), prime q = 4n2 + 1, and the class number of quadratic number field K2 = Q(vq) is 1.In this paper we use Dedekind zeta functions of two real quadratic number fields at -1 to denote Dedekind sums of high rank. Our formula is different from that of Siegel's. As an application, we get a polynomial representation of ζK(-1): ζK(-1) =1/45(26n3-41n±9), n ≡±2(mod 5), where K=Q( q),prime q=4n2+1, and the class number of quadratic number field K2=Q(q) is 1.

关 键 词：QUADRATIC number fields  DEDEKIND ZETA functions  DEDEKIND sums. 

分 类 号：O156[理学—数学]