Title: L-functions and sharp resonances of infinite index congruence subgroups of $SL_2(\mathbb{Z})$,
Abstract: For convex co-compact subgroups of SL2(Z) we consider the "congruence
subgroups" for p prime. We prove a factorization formula for the Selberg zeta
function in term of L-functions related to irreducible representations of the
Galois group SL2(Fp) of the covering, together with a priori bounds and
analytic continuation. We use this factorization property combined with an
averaging technique over representations to prove a new existence result of
non-trivial resonances in an effective low frequency strip.