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arXiv · 1810.06254

Hypergeometric decomposition of symmetric K3 quartic pencils

Charles F. Doran·Tyler L. Kelly·Adriana Salerno·Steven Sperber·John Voight·Ursula Whitcher
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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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Charles F. Doran, Tyler L. Kelly, Adriana Salerno, Steven Sperber, John Voight, Ursula Whitcher. 2018-10-15. Hypergeometric decomposition of symmetric K3 quartic pencils. https://arxiv.org/abs/1810.06254

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