3 papers
math.NT2026
On the prime geodesic theorem
Alberto Acosta Reche
We improve the error term in the prime geodesic theorem for the modular group. More generally, our result applies to any congruence subgroup of any indefinite quaternion algebra ov…
math.NT2026
Chebotarev geodesic theorem: non-split case
Alberto Acosta Reche
We study the prime geodesic theorem for congruence subgroups of indefinite quaternion orders. We prove that the geodesic analogue of the Chebotarev density theorem for these groups…
math.NT2026
Chebotarev geodesic theorem: split case
Alberto Acosta Reche
We study the prime geodesic theorem in congruence classes of . We generalize previous work of Luo and Sarnak and of Soundararajan and Young, and prove th…