Distinguished-root formulas for generalized Calabi-Yau hypersurfaces

Alan Adolphson, Steven Sperber

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


By a “generalized Calabi-Yau hypersurface” we mean a hypersurface in ℙn of degree d dividing n C1. The zeta function of a generic such hypersurface has a reciprocal root distinguished by minimal p-divisibility. We study the p-adic variation of that distinguished root in a family and show that it equals the product of an appropriate power of p times a product of special values of a certain p-adic analytic function F. That function F is the p-adic analytic continuation of the ratio F.(Λ)=F.(Λp), where F.(Λ) is a solution of the A-hypergeometric system of differential equations corresponding to the Picard-Fuchs equation of the family.

Original languageEnglish (US)
Pages (from-to)1317-1356
Number of pages40
JournalAlgebra and Number Theory
Issue number6
StatePublished - 2017

Bibliographical note

Publisher Copyright:
© 2017 Mathematical Sciences Publishers.


  • A-hypergeometric system
  • Calabi-yau
  • P-adic analytic function
  • Zeta function


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