Hypergeometric decomposition of symmetric K3 quartic pencils

2018/10/15 by Doran, Charles F., Kelly, Tyler L., Salerno, Adriana +3 · 1 citation
#11G40 #11S40 #11T24 #14J28 #33C20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1810.06254

Abstract

We study the hypergeometric functions associated to five one-parameter deformations of Delsarte K3 quartic hypersurfaces in projective space. We compute all of their Picard--Fuchs differential equations; we count points using Gauss sums and rewrite this in terms of finite field hypergeometric sums; then we match up each differential equation to a factor of the zeta function, and we write this in terms of global L-functions. This computation gives a complete, explicit description of the motives for these pencils in terms of hypergeometric motives.

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