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<p>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 <i>L</i>-function of each pencil in terms of hypergeometric <i>L</i>-series and Dedekind zeta functions. This gives an explicit description of the hypergeometric motives geometrically realized by each pencil.</p>

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Hypergeometric decomposition of Delsarte K3 pencils

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月23日

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  • Rachel Davis,
  • Jessamyn Dukes,
  • Thais Gomes Ribeiro,
  • Eli Orvis,
  • Adriana Salerno,
  • Leah Sturman,
  • Ursula Whitcher

摘要

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.