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-   -   Question about Selberg Zeta. (http://www.physicsforums.com/showthread.php?t=324996)

zetafunction Jul14-09 07:35 AM

Question about Selberg Zeta.
 
given the Selberg trace formula

[tex] \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 ) [/tex]

then i have the question if [tex] \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) [/tex] is correct

with [tex] Z(s) [/tex] is the Selberg Zeta function.


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