Аннотация:
The “Chebotarev Prime Geodesic Theorem” for primitive
conjugacy classes in $\mathrm{SL}(2 , \mathbb{Z})$ (which correspond to closed geodesics
on the quotient) is well known and can be proved using the Selberg Trace
Formula. We examine local versions of this Theorem where
the closed geodesics are restricted in various ways and in particular to
being simple. Congruence and arithmetic features intervene decisively
as well as transitivity properties of the action of associated mapping class groups.
