English

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

Spectral Theory 2014-09-10 v1 Number Theory

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 (s)=δ/2\Re(s)=\delta/2.

Keywords

Cite

@article{arxiv.1409.2809,
  title  = {Resonances and convex co-compact congruence subgroups of PSL2(Z)},
  author = {Frédéric Naud and Dmitry Jakobson},
  journal= {arXiv preprint arXiv:1409.2809},
  year   = {2014}
}