Zeta functions of alternate mirror Calabi–Yau families

Research output: Contribution to journalArticlepeer-review

Authors

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

Colleges, School and Institutes

External organisations

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

Abstract

We prove that if two Calabi–Yau invertible pencils have the same dual weights, then they share a common factor in their zeta functions. By using Dwork cohomology, we demonstrate that this common factor is related to a hypergeometric Picard–Fuchs differential equation. The factor in the zeta function is defined over the rationals and has degree at least the order of the Picard–Fuchs equation. As an application, we relate several pencils of K3 surfaces to the Dwork pencil, obtaining new cases of arithmetic mirror symmetry.

Details

Original languageEnglish
Pages (from-to)665–705
Number of pages41
JournalIsrael Journal of Mathematics
Volume228
Issue number2
Early online date26 Sep 2018
Publication statusPublished - Oct 2018