Hypergeometric Decomposition of Symmetric K3 Quartic Pencils

Charles Doran, Tyler Kelly, Adriana Salerno, Steven Sperber, John Voight, Ursula Whitcher

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
116 Downloads (Pure)

Abstract

We study the hypergeometric functions associated to five one-parameter deformations of Delsarte K3 quartic hypersurfaces in projective space. We compute all of their Picard--Fuchs differential equations; we count points using Gauss sums and rewrite this in terms of finite field hypergeometric sums; then we match up each differential equation to a factor of the zeta function, and we write this in terms of global $L$-functions. This computation gives a complete, explicit description of the motives for these pencils in terms of hypergeometric motives.
Original languageEnglish
Article number7
Number of pages70
JournalResearch in the Mathematical Sciences
Volume7
Issue number2
Early online date16 Mar 2020
DOIs
Publication statusE-pub ahead of print - 16 Mar 2020

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Mathematics (miscellaneous)
  • Computational Mathematics
  • Applied Mathematics

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