Year: 2026
Type: article
Abstract: We study five pencils of projective quartic Delsarte K3 surfaces. Over finite fields, we give explicit formulas for the point counts of each family, written in terms of hypergeometric sums. Over the complex numbers, we match the periods of the corresponding family with hypergeometric differential operators and series. We also obtain a decomposition of the incomplete L -function of each pencil in terms of hypergeometric L -series and Dedekind zeta functions. This gives an explicit description of the hypergeometric motives geometrically realized by each pencil.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,090
OpenAlex ID: W7162188766