基于M.Katsurada所得zeta函数狄利克雷级数系数的模关系解释  

Modular relation theoretic interpretation of M.Katsurada′s Dirichlet series of zeta function

作　　者：陈小芳 金光滋 李海龙 CHEN Xiaofang;KANEMITSU S;LI Hailong(School of Mathematics and physics, Weinan Normal University, Weinan 714099, Shaanxi, China;Department of Applied Seience,Kyushu Institute of Technology,Kitakyushu 8048555, Japan)

机构地区：[1]渭南师范学院数理学院,陕西渭南714099 [2]九州技术研究中心应用科学系,日本北九州8048555

出　　处：《陕西师范大学学报（自然科学版）》2018年第4期21-27,共7页Journal of Shaanxi Normal University：Natural Science Edition

基　　金：国家自然科学基金(11501419);陕西省军民融合项目(16JMR11);渭南师范学院科研项目(17YKS11)

摘　　要：研究模关系理论与M.Katsurada的关于zeta函数系数级数的结论之间的关系,用模关系理论对Katsurada的zeta函数狄利克雷级数系数的一些研究结果进行解释。证明了一个一般性定理,该定理包含Katsurada的两个定理,可将M.Katsurada的Riesz和结论解释为一种模关系,还证明M.Katsurada的快速收敛级数表达式也是一种模关系。其中Ψ-函数在研究中发挥了至关重要的作用,该函数也出现在Bochner-Chandrasekharan的一些研究中。making a modular-relation-theoretic interpretation of some of Katsurada＇s results on the series of zeta-function coefficients, a general theorem is proved which entails two of Katsurada＇s theorems to the effect that his results amount to the Reisz sum,it can be interpreted as a modular relation. A rather remarkable result is proved that another of its rapidly convergent series expression is also a modular relation. An essential role is played by the x/z-function, which also appeared in the context of Bochner-Chandrasekharan＇s investigations.

关 键 词：ZETA函数 模关系 Riesz和 Riesz核 Riesz均值 

分 类 号：O156.7[理学—数学]