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

Daniel Loughran; Judith Ortmann

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

Daniel Loughran, Judith Ortmann

Department of Mathematical Sciences

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Abstract

Serre famously showed that almost all plane conics over Q have no rational point. We investigate versions of this over global function fields, focusing on a specific family of conics over F 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.

Original language	English
Journal	Mathematische Nachrichten
Publication status	Acceptance date - 4 Sept 2025

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2412.14693v2Accepted author manuscript, 581 KB

https://arxiv.org/abs/2412.14693

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

Abstract

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