Prime Geodesic Theorem for Arithmetic Compact Surfaces: Principal Congruence Case
Abstract
Abstract We generalize Koyama’s $7/10$ bound of the error term in the prime geodesic theorems to the principal congruence subgroups for quaternion algebras. Our method avoids the spectral side of the Jacquet–Langlands correspondences, and relates the counting function directly to those for the principal congruence subgroups of Eichler orders of level less than one.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Differential Equations and Dynamical Systems
History and Theory of Mathematics
Publication details
- Journal / source
- International Mathematics Research Notices
- Volume
- 2026
- Issue
- 8
- Publication date
- 18 March 2026
- Language
- EN