关于类似广义Dedekind和S_2(h,m,n,k)的几个恒等式

On some identities of the sum analogous to the generalized Dedekind sum S_2(h,m,n,k)

利用初等方法研究了类似广义Dedekind和S2(h,m,n,k)的算术性质.借助Bernoulli多项式及三角恒等式,探究了S2(qh,m,n,qk)与S2(h,m,n,k)的关系,以及当p为奇素数时sum from b=0 to (p-1) S2(h+bk,m,n,pk)与S2(h,m,n,k)和S2(ph,m,n,k)的关系,提出并证明了两个恒等式,推广了有关文献的结论.

The arithmetic properties for a sum analogous to the generalized Dedekind are studied by using elementary method. With the Bernoulli polynomial and trigonometric identity, the relationship are studied between S2（qh,m,n,qk） andS2（h,m,n,k）, ∑b=0^p-1 S2 （h ＋bk,m,n,pk） and S2 （h,m,n,k） and S2（ph,m,n,k） ,when p is a odd prime . Two identities are given and proved, the conclusions are extended in some references.