Resonances and convex co-compact congruence subgroups of PSL2(Z)

Frédéric Naud (1) , Dmitry Jakobson (2)

1 LANLG - Laboratoire d'Analyse non linéaire et Géométrie
2 McGill University = Université McGill [Montréal, Canada]

This papers deals with congruence subgroups of convex cocompact subgroups of PSL2(Z). We examine the behaviour of the resonance spectrum when the congruence parameter q goes to infinity: we show a lower bound for the counting function in discs and an upper bound in vertical strips. These results show drastically different behaviour on both sides of the critical line $\Re(s)=\delta/2$.

Mots clés: Selberg's zeta function; Hyperbolic surfaces; congruence subgroups; resonances; Selberg's zeta function.

Domaines: Théorie spectrale [math.SP]; Théorie des nombres [math.NT]

Frédéric Naud, Dmitry Jakobson. Resonances and convex co-compact congruence subgroups of PSL2(Z). 2014. ⟨hal-01061897⟩