Rational points in a family of conics over $\mathbb{F}_2(t)$
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911137608499200 |
|---|---|
| author | Loughran, Daniel Ortmann, Judith |
| author_facet | Loughran, Daniel Ortmann, Judith |
| contents | Serre famously showed that almost all plane conics over $\mathbb{Q}$ have no rational point. We investigate versions of this over global function fields, focusing on a specific family of conics over $\mathbb{F}_2(t)$ which illustrates new behaviour. We obtain an asymptotic formula using harmonic analysis, which requires a Tauberian theorem over function fields for Dirichlet series with branch point singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14693 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rational points in a family of conics over $\mathbb{F}_2(t)$ Loughran, Daniel Ortmann, Judith Number Theory 14G05 (primary), 14F22 (secondary) Serre famously showed that almost all plane conics over $\mathbb{Q}$ have no rational point. We investigate versions of this over global function fields, focusing on a specific family of conics over $\mathbb{F}_2(t)$ which illustrates new behaviour. We obtain an asymptotic formula using harmonic analysis, which requires a Tauberian theorem over function fields for Dirichlet series with branch point singularities. |
| title | Rational points in a family of conics over $\mathbb{F}_2(t)$ |
| topic | Number Theory 14G05 (primary), 14F22 (secondary) |
| url | https://arxiv.org/abs/2412.14693 |