1. ### zetafunction

399
given the Selberg trace formula

$$\sum_{n=0}^{\infty} h(r_n) = \frac{\mu(F)}{4 \pi } \int_{-\infty}^{\infty} r \, h(r) \tanh(\pi r) dr + \sum_{ \{T\} } \frac{ \log N(T_0) }{ N(T)^{1/2} - N(T)^{-1/2} } g \left ( \log N(T) \right )$$

then i have the question if $$\frac{ Z'}{Z}(1/2+is) = \sum_{ \{T\} } \frac{ \log N(T_0) }{ N(T)^{1/2} - N(T)^{-1/2} } exp(ilog(N (T_0)$$ is correct

with $$Z(s)$$ is the Selberg Zeta function.