Publikationsdetails
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
- Organisationseinheit(en)
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Institut für Algebra, Zahlentheorie und Diskrete Mathematik
- Typ
- Preprint
- Publikationsdatum
- 19.12.2024
- Publikationsstatus
- Elektronisch veröffentlicht (E-Pub)
- Elektronische Version(en)
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https://doi.org/10.48550/arXiv.2412.14693 (Zugang:
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