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

Davide Lombardo; Francesco Ballini; Matteo Verzobio

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arxiv 1807.07370 v4 pith:LSNZ3EM2 submitted 2018-07-19 math.NT math.AG

On the L-polynomials of curves over finite fields

Francesco Ballini , Davide Lombardo , Matteo Verzobio This is my paper

classification math.NT math.AG

keywords curvespolynomialsdistributionfieldsfinitemathbballowsarchimedean

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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.

On the L-polynomials of curves over finite fields

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