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

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 $\Re(s)=\delta/2$.
Keywords :
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-01061897
Contributor : Frédéric Naud <>
Submitted on : Monday, September 8, 2014 - 4:54:10 PM
Last modification on : Friday, March 22, 2019 - 11:48:12 AM
Long-term archiving on : Tuesday, December 9, 2014 - 12:37:28 PM

### Files

SharpReso.pdf
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### Identifiers

• HAL Id : hal-01061897, version 1
• ARXIV : 1409.2809

### Citation

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

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