On the L-polynomials of curves over finite fields
Authors:
- Francesco BalliniFBFrancesco Ballini
- Davide LombardoDLDavide Lombardo
- Matteo VerzobioMVMatteo Verzobio
Open Access
- 6 February 2025
- journal article
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- p. 1-49
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.
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