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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.05659 |
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| _version_ | 1866915867656192000 |
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| author | Tang, Chenhao Wu, Han Yang, Jie Yang, Wenyan |
| author_facet | Tang, Chenhao Wu, Han Yang, Jie Yang, Wenyan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05659 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Prime Geodesic Theorem for Arithmetic Compact Surfaces: Principal Congruence Case Tang, Chenhao Wu, Han Yang, Jie Yang, Wenyan Number Theory 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. |
| title | Prime Geodesic Theorem for Arithmetic Compact Surfaces: Principal Congruence Case |
| topic | Number Theory |
| url | https://arxiv.org/abs/2510.05659 |