Hypergeometric decomposition of Delsarte K3 pencils
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918476611846144 |
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| author | Davis, Rachel Dukes, Jessamyn Ribeiro, Thais Gomes Orvis, Eli Salerno, Adriana Sturman, Leah Whitcher, Ursula |
| author_facet | Davis, Rachel Dukes, Jessamyn Ribeiro, Thais Gomes Orvis, Eli Salerno, Adriana Sturman, Leah Whitcher, Ursula |
| contents | 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 $L$-function of each pencil in terms of hypergeometric $L$-series and Dedekind zeta functions. This gives an explicit description of the hypergeometric motives geometrically realised by each pencil. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_15049 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hypergeometric decomposition of Delsarte K3 pencils Davis, Rachel Dukes, Jessamyn Ribeiro, Thais Gomes Orvis, Eli Salerno, Adriana Sturman, Leah Whitcher, Ursula Number Theory Algebraic Geometry 11S40 (11G40, 11T24, 14G10, 14J28, 32G34, 33C80, 33E50) 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 $L$-function of each pencil in terms of hypergeometric $L$-series and Dedekind zeta functions. This gives an explicit description of the hypergeometric motives geometrically realised by each pencil. |
| title | Hypergeometric decomposition of Delsarte K3 pencils |
| topic | Number Theory Algebraic Geometry 11S40 (11G40, 11T24, 14G10, 14J28, 32G34, 33C80, 33E50) |
| url | https://arxiv.org/abs/2508.15049 |