Rational points in a family of conics over 𝔽2(t)

Daniel Loughran; Judith Ortmann

doi:10.1002/mana.70038

Rational points in a family of conics over 𝔽₂(t)

Daniel Loughran, Judith Ortmann

Department of Mathematical Sciences

Leibniz Universität Hannover

Research output: Contribution to journal › Article › peer-review

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Abstract

Serre famously showed that almost all plane conics over (Formula presented.) have no rational point. We investigate versions of this over global function fields, focusing on a specific family of conics over (Formula presented.) which illustrates new behavior. We obtain an asymptotic formula using harmonic analysis, which requires a Tauberian theorem over function fields for Dirichlet series with branch point singularities.

Original language	English
Pages (from-to)	496-513
Journal	Mathematische Nachrichten
Volume	299
Issue number	3
Early online date	8 Feb 2026
DOIs	https://doi.org/10.1002/mana.70038
Publication status	E-pub ahead of print - 8 Feb 2026

Bibliographical note

AAM arXiv

Funding

UK Research and Innovation. Grant Number: MR/V021362/1 Caroline Herschel Programme of Leibniz University Hannover UKRI Future Leaders Fellowship. Grant Number: MR/V021362/1

Keywords

conics
function fields
harmonic analysis
rational points

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1002/mana.70038Licence: CC BY

2412.14693v2Accepted author manuscript, 581 KB

https://arxiv.org/abs/2412.14693

Cite this

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