Hypergeometric decomposition of Delsarte K3 pencils
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.
Authors
- Rachel Davis
- Jessamyn Dukes
- Adriana Salerno
- Leah Sturman
- Ursula Whitcher
- Thais Gomes Ribeiro (ORCID: https://orcid.org/0009-0001-3486-4830)
- Eli Orvis
Institutions
- U.S. National Science Foundation (US)
- University of Denver (US)
- University of Wisconsin–Madison (US)
- University of Colorado Boulder (US)
- Southern Connecticut State University (US)
- American Mathematical Society (US)
- University of Birmingham (GB)
Publication Details
- Journal
- Research in the Mathematical Sciences
- Published
- 2026-05-23
- DOI
- https://doi.org/10.1007/s40687-026-00634-x
- Primary Topic
- Algebraic Geometry and Number Theory
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- University of Birmingham