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Journal of the Ramanujan Mathematical Society

Volume 37, Issue 4, December 2022  pp. 385–409.

Frobenius trace distributions for K3 surfaces

Authors:  Andreas-Stephan Elsenhans and Jörg Jahnel
Author institution: Institut für Mathematik, Universität Würzburg, Emil-Fischer-Straße 30, D-97074 Würzburg, Germany

Summary:  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. Each time, the theoretical density and the histogram obtained by counting points match in the range of visible accuracy. Thus, we report evidence for the Sato–Tate conjecture for the surfaces considered.

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