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

2014/09/09 by Frédéric Naud, Dmitry Jakobson, Naud, Frédéric +1
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #Spectral Theory (math.SP) #math.NT #math.SP

paper · pdf · doi:10.48550/arxiv.1409.2809

arxiv created 2014/09/09 · arxiv updated 2014/09/10

Abstract

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)=δ/2.

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