Abstract:We study the prime geodesic theorem in congruence classes of $\mathrm{SL}_2(\mathbb{Z})$. We generalize previous work of Luo and Sarnak and of Soundararajan and Young, and prove that the geodesic analogue of the Chebotarev density theorem holds with exponent $25/36 + \varepsilon$. In particular, we deduce that the prime geodesic theorem holds with exponent $25/36 + \varepsilon$ for any congruence subgroup of $\mathrm{SL}_2(\mathbb{Z})$.
From: Alberto Acosta Reche [view email]
[v1]
Wed, 24 Jun 2026 14:52:05 UTC (69 KB)
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