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May 25, 2026Research in the Mathematical SciencesOpen Access

Hypergeometric decomposition of Delsarte K3 pencils

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Authors

RDRachel DavisJDJessamyn DukesTRThais Gomes Ribeiro

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Overview

Reports hypergeometric formulas for point counts in Delsarte K3 surfaces, suggesting deep connections in algebraic geometry.

Key Points

  • The aim is to analyze Delsarte K3 surfaces and their associated hypergeometric structures.
  • Investigated five families of projective quartic Delsarte K3 surfaces.
  • Calculated point counts over finite fields using hypergeometric sums.
  • Analyzed periods using hypergeometric differential operators and series.
  • Explicit formulas for point counts in each family based on hypergeometric sums were derived.
  • Established connections between hypergeometric differential operators and the families' periods.
  • Decomposed the incomplete L-function of each pencil into hypergeometric L-series and Dedekind zeta functions.

Cite This Study

Davis et al. (2026) studied this question.

synapsesocial.com/papers/6a13e78b0e02ee3982d323efhttps://doi.org/10.1007/s40687-026-00634-x
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