Frobenius trace distributions for K3 surfaces
2021
We study the distribution of the Frobenius traces on $K3$ surfaces. We compare experimental data with the predictions made by the Sato--Tate conjecture, i.e. with the theoretical distributions derived from the theory of Lie groups assuming equidistribution. Our sample consists of generic $K3$ surfaces, as well as of such having real and complex multiplication. We report evidence for the Sato--Tate conjecture for the surfaces considered.
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