Modular relation theoretic interpretation of M. Katsurada′s Dirichlet series of zeta function
CHEN Xiaofang1, KANEMITSU S2*, LI Hailong1
(1 School of Mathematics and physics,Weinan Normal University,Weinan 714099，Shaanxi,China;2 Department of Applied Science,Kyushu Institute of Technology,Kitakyushu 8048555, Japan)
Abstract:
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 Ψ-function, which also appeared in the context of Bochner-Chandrasekharan′s investigations.
KeyWords:
zeta-function; modular relation; Reisz sum; Reisz kernel; Riesz mean
