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Case g = 2 and q = 101. The red dots are the values of H . The black stars are the values of the approximation of ν (q, t). The blue graph is the approximation of the Sato-Tate density. In this case, d(H , ν ) ≈ 0.01117 and d(H , ν∞) ≈ 0.15166.

Case g = 2 and q = 101. The red dots are the values of H . The black stars are the values of the approximation of ν (q, t). The blue graph is the approximation of the Sato-Tate density. In this case, d(H , ν ) ≈ 0.01117 and d(H , ν∞) ≈ 0.15166.

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Figure 1. Case g = 2 and q = 1009. The red dots are the values of H ....
Figure 2. Case g = 2 and q = 101. The red dots are the values of H ....
Figure 3. Case g = 3 and q = 53. The red dots are the values of H . The...
Figure 4. Case g = 2 and q = 5. As pointed out in remark 3.9, there is...
On the L -polynomials of curves over finite fields
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  • Feb 2025
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 t...
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... an orthonormal basis of L 2 ([−2g, 2g]). From the explicit expression of˜Lof˜ of˜L n (x) = n i=0 a n,i x i as a polynomial, one can easily compute ...