On Jordan Double Sums and Related Summatory Functions

We study the Jordan double sums ∑[ d,δ ]≤NJɛ(d)Jɛ(δ)[ d,δ ]σ+2ɛ+it, \sum\limits_{\left[ {d,\delta } \right] \le N} {{{{J_\varepsilon }\left( d \right){J_\varepsilon }\left( \delta \right)} \over {{{\left[ {d,\delta } \right]}^{\sigma + 2\varepsilon + it}}}},} which are connected with usual zeta approximating sums. Some other related summatory functions involving Jordan’s function are considered and estimated in this paper.