J. Gasnier

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20232026

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math.NT2025

Unramified abelian covers with many points

Jean Gasnier

We produce curves with a record number of points over the finite fields with $4$ , $9$ , $16$ and $25$ elements, as unramified abelian covers of algebraic curves.

math.NT2023

Explicit Riemann-Roch spaces in the Hilbert class field

Jean-Marc Couveignes, Jean Gasnier

Let $K$ be a finite field, $X$ and $Y$ two curves over $K$ , and $Y \to X$ an unramified abelian cover with Galois group $G$ . Let $D$ be a divisor on $X$ and…