Even and Odd Integer Values of the Secondary Zeta Function

The secondary zeta function is defined by $$ Z(s)=\sum_{γ>0}\frac{1}{γ^{s}}, $$ where $\tfrac12+iγ$ runs over the non-trivial zeros of the Riemann zeta function with positive ordinate, and the Riemann hypothesis is assumed throughout. In this article, we derive convergent integral representations of