zetafunction
Jul14-09, 08:35 AM
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.
\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.