Farey neighbours, modular symbols and divergent geodesics
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911134292901888 |
|---|---|
| author | Parkkonen, Jouni Paulin, Frédéric |
| author_facet | Parkkonen, Jouni Paulin, Frédéric |
| contents | We give effective asymptotic counting results for pairs of Farey neighbours and for modular symbols in $\mathbb Q$, in imaginary quadratic number fields and in definite quaternion algebras over $\mathbb Q$, using the distribution of common perpendiculars between Margulis cusp neighbourhoods and divergent geodesics in hyperbolic manifolds. We describe the tangency properties of the canonical Margulis cusp neighbourhoods in Bianchi hyperbolic $3$-orbifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02269 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Farey neighbours, modular symbols and divergent geodesics Parkkonen, Jouni Paulin, Frédéric Number Theory 11B57, 20H10, 11N45, 53C22, 11R04, 22E40 We give effective asymptotic counting results for pairs of Farey neighbours and for modular symbols in $\mathbb Q$, in imaginary quadratic number fields and in definite quaternion algebras over $\mathbb Q$, using the distribution of common perpendiculars between Margulis cusp neighbourhoods and divergent geodesics in hyperbolic manifolds. We describe the tangency properties of the canonical Margulis cusp neighbourhoods in Bianchi hyperbolic $3$-orbifolds. |
| title | Farey neighbours, modular symbols and divergent geodesics |
| topic | Number Theory 11B57, 20H10, 11N45, 53C22, 11R04, 22E40 |
| url | https://arxiv.org/abs/2509.02269 |