Selberg Zeta Function Selberg Trace Formula Degenerating Hyperbolic Manifolds
Bulgarian Academy of Sciences - National Committee for Mathematics
Mathematica Balkanica New Series, Vol. 24, Fasc 3-4 (2010), 243p-251p
We point out the importance of the integral representations of the logarithmic derivative of the Selberg zeta function valid up to the critical line, i.e. in the region that includes the right half of the critical strip, where the Euler product deﬁnition of the Selberg zeta function does not hold. Most recent applications to the behavior of the Selberg zeta functions associated to a degenerating sequence of ﬁnite volume, hyperbolic manifolds of dimension 2 and 3 are surveyed. The research problem consists in extending this kind of integral representations to the setting of the locally symmetric spaces of rank 1.