On the <i>L</i>-polynomials of curves over finite fields
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.
Authors
- Matteo Verzobio (ORCID: https://orcid.org/0000-0002-0854-0306)
- Davide Lombardo (ORCID: https://orcid.org/0000-0002-1069-3379)
- Francesco Ballini (ORCID: https://orcid.org/0000-0002-6495-196X)
Institutions
- University of Pisa (IT)
- Institute of Science and Technology Austria (AT)
- Mathematical Institute of the Slovak Academy of Sciences (SK)
Publication Details
- Journal
- Proceedings of the Royal Society of Edinburgh Section A Mathematics
- Published
- 2025-02-06
- DOI
- https://doi.org/10.1017/prm.2025.7
- Primary Topic
- Algebraic Geometry and Number Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- European Commission
- Ministero dell’Istruzione, dell’Università e della Ricerca
- Università di Pisa