In this paper, by making use of Abel’s theorem on power series, the reflection formula and the function equation for Hurwitz zeta function, we establish several expressions of Dirichlet Lfunction at positive integers...In this paper, by making use of Abel’s theorem on power series, the reflection formula and the function equation for Hurwitz zeta function, we establish several expressions of Dirichlet Lfunction at positive integers by means of some finite sums of different types. Some special cases as well as immediate consequences of the results presented here are also considered.展开更多
Mare Chamberland和Karl Dilcher[Divisibility properties of a class of binomial sums,J.Number Theory,120(2006)pp.349-371]研究了一类二项式和uεa,b(n)并给出了一些有趣的性质,其中uεa,b(n)=∑nk=0(-1)εk(kn)a(2kn)b,对a,b,n∈...Mare Chamberland和Karl Dilcher[Divisibility properties of a class of binomial sums,J.Number Theory,120(2006)pp.349-371]研究了一类二项式和uεa,b(n)并给出了一些有趣的性质,其中uεa,b(n)=∑nk=0(-1)εk(kn)a(2kn)b,对a,b,n∈N和ε∈{0,1}.最后,他们提出了uaε,b(n)的一种推广,即uεa,b,c(n)=∑nk=0(-1)εk(kn)a(2kn)b(3kn)c,其中a,b,c,n∈N,ε∈{0,1},期望uεa,b,c(n)具有与uaε,b(n)相似的性质,但并未给出具体的性质及证明.在本文中,我们给出并证明了uεa,b,c(n)的与Wolstenhol me定理有关的这部分性质.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11326050)
文摘In this paper, by making use of Abel’s theorem on power series, the reflection formula and the function equation for Hurwitz zeta function, we establish several expressions of Dirichlet Lfunction at positive integers by means of some finite sums of different types. Some special cases as well as immediate consequences of the results presented here are also considered.
文摘Mare Chamberland和Karl Dilcher[Divisibility properties of a class of binomial sums,J.Number Theory,120(2006)pp.349-371]研究了一类二项式和uεa,b(n)并给出了一些有趣的性质,其中uεa,b(n)=∑nk=0(-1)εk(kn)a(2kn)b,对a,b,n∈N和ε∈{0,1}.最后,他们提出了uaε,b(n)的一种推广,即uεa,b,c(n)=∑nk=0(-1)εk(kn)a(2kn)b(3kn)c,其中a,b,c,n∈N,ε∈{0,1},期望uεa,b,c(n)具有与uaε,b(n)相似的性质,但并未给出具体的性质及证明.在本文中,我们给出并证明了uεa,b,c(n)的与Wolstenhol me定理有关的这部分性质.
