Work

On the L-polynomials of curves over finite fields

Year: 2025

Type: article

Abstract: We discuss, in a non-Archimedean setting, the distribution of the coefficients of L-polynomials of curves of genus g over $\mathbb{F}_q$ . Among other results, this allows us to prove that the $\mathbb{Q}$ -vector space spanned by such characteristic polynomials has dimension g + 1. We also state a conjecture about the Archimedean distribution of the number of rational points of curves over finite fields.

Source: Proceedings of the Royal Society of Edinburgh Section A Mathematics

DOI: 10.1017/prm.2025.7

Authors: Francesco Ballini, Davide Lombardo, Matteo Verzobio

Institutions: University of Oxford, University of Pisa, Institute of Science and Technology Austria

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: European Commission, Ministero dell’Istruzione, dell’Università e della Ricerca, Università di Pisa