Fernando Rodriguez-Villegas has conjectured a number of supercongruences for hypergeometric Calabi-Yau manifolds of dimension d ≤ 3. For manifolds of dimension d = 1, he observed four potential supercongruences. Later the author proved one of the four. Motivated by Rodriguez-Villegas's work, in the present paper we prove a general result on supercongruences between values of truncated 2F1 hypergeometric functions and Gaussian hypergeometric functions. As a corollary to that result, we prove the three remaining supercongruences.
Original languageEnglish
Pages (from-to)987-1007
Number of pages21
JournalTransactions of the American Mathematical Society
Volume355
Issue number3
DOIs
StatePublished - 1 Mar 2003

    Research areas

  • Supercongruences

ID: 126316842