On the $L$-polynomials of curves over finite fields
Number Theory
2025-07-25 v4 Algebraic Geometry
Abstract
We discuss, in a non-Archimedean setting, the distribution of the coefficients of -polynomials of curves of genus over . Among other results, this allows us to prove that the -vector space spanned by such characteristic polynomials has dimension . We also state a conjecture about the Archimedean distribution of the number of rational points of curves over finite fields.
Keywords
Cite
@article{arxiv.1807.07370,
title = {On the $L$-polynomials of curves over finite fields},
author = {Francesco Ballini and Davide Lombardo and Matteo Verzobio},
journal= {arXiv preprint arXiv:1807.07370},
year = {2025}
}
Comments
v4: Accepted version, to appear in Proceedings of the Royal Society of Edinburgh. At the suggestion of a referee we removed the appendix, which is still available as part of v3 of this paper here on the ArXiv