For K3 surfaces, we derive some conditions the characteristic polynomial of the Frobenius on the étale cohomology must satisfy. These conditions may be used to speed up the computation of Picard numbers and the decision of the sign in the functional equation**. Our investigations are based on the Artin-Tate formula. © 2010 Springer-Verlag Berlin Heidelberg.
Elsenhans, A. S., & Jahnel, J. (2010). On Weil polynomials of K3 surfaces. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6197 LNCS, pp. 126–141). https://doi.org/10.1007/978-3-642-14518-6_13