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Mathematics > Number Theory

arXiv:1807.07370 (math)
[Submitted on 19 Jul 2018 (v1), last revised 15 Feb 2024 (this version, v3)]

Title:On the $L$-polynomials of curves over finite fields

Authors:Francesco Ballini, Davide Lombardo, Matteo Verzobio
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Abstract:We discuss, in a non-archimedean setting, the distribution of the coefficients of L-polynomials of curves of genus $g$ over $\mathbb{F}_q$. This allows us to prove, among other things, 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.
Comments: Second version: added several results concerning the non-archimedean distribution of L-polynomials and a conjecture about the distribution of the number of points of curves over finite fields. Two authors added. v3: Clarified relation with a conjecture of Bergström, Howe, Lorenzo-García, and Ritzenthaler; acknowledgements updated. 38 pages
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
MSC classes: 11F80, 11G20, 11G10
Cite as: arXiv:1807.07370 [math.NT]
  (or arXiv:1807.07370v3 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1807.07370

Submission history

From: Davide Lombardo [view email]
[v1] Thu, 19 Jul 2018 12:49:54 UTC (6 KB)
[v2] Tue, 16 Jan 2024 07:16:41 UTC (47 KB)
[v3] Thu, 15 Feb 2024 10:20:30 UTC (51 KB)
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