Rational points in a family of conics over F2(t)
Abstract
Abstract Serre famously showed that almost all plane conics over have no rational point. We investigate versions of this over global function fields, focusing on a specific family of conics over 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.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Algebraic Geometry and Number Theory
Polynomial and algebraic computation
Publication details
- Journal / source
- Mathematische Nachrichten
- Volume
- 299
- Issue
- 3
- Pages
- 496–513
- Publication date
- 8 February 2026
- Language
- EN