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arXiv · 1704.08546

L-functions and sharp resonances of infinite index congruence subgroups of $SL_2(\mathbb{Z})$

Dmitry Jakobson·Frederic Naud
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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.

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Dmitry Jakobson, Frederic Naud. 2017-04-27. L-functions and sharp resonances of infinite index congruence subgroups of $SL_2(\mathbb{Z})$. https://arxiv.org/abs/1704.08546

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