Publication details
Rational points in a family of conics over 𝔽𝟸(𝑡)
Abstract
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 new Tauberian theorem over function fields for Dirichlet series with branch point singularities.
Details
- Organisation(s)
-
Institute of Algebra, Number Theory and Discrete Mathematics
- Type
- Preprint
- Publication date
- 19.12.2024
- Publication status
- E-pub ahead of print
- Electronic version(s)
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https://doi.org/10.48550/arXiv.2412.14693 (Access:
Open
)
