On the secondary zeta-functions

Using summability it is shown that $\text{∑}{}_{\mathrm{n}}\text{?2 (Λ(n) ? 1) n}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{(log n)}{}^{\mathrm{?8}}$ defines an entire function in the s-plane. Its asymptotic nature is found and a functional equation relating it to the series $\text{∑{i(}\text{1}\text{2}\text{? p)}}{}^{\mathrm{1?8}}$, Im p = γ > 0,is obtained where p = β + iγ are the nontrivial zeros of Riemann's zeta-function.