Hypergeometric Decomposition of Symmetric K3 Quartic Pencils

Research output: Contribution to journalArticle

Authors

  • Charles Doran
  • Adriana Salerno
  • Steven Sperber
  • John Voight
  • Ursula Whitcher

Colleges, School and Institutes

External organisations

  • University of Alberta
  • University of Minnesota, Minneapolis, Minnesota 55455, USA
  • DARTMOUTH COLLEGE
  • Mathematical Reviews

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.

Details

Original languageEnglish
Number of pages70
JournalResearch in the Mathematical Sciences
Publication statusAccepted/In press - 22 Jan 2020