Supercongruences between truncated $_{2}F_{1}$ hypergeometric functions and their Gaussian analogs
Copyright policy )Supercongruences between truncated $_{2}F_{1}$ hypergeometric functions and their Gaussian analogs
\textit{F. Rodriguez-Villegas} [Hypergeometric families of Calabi-Yau manifolds, Yui, Noriko (ed.) et al., Calabi-Yau varieties and mirror symmetry. Providence, RI: American Mathematical Society (AMS). Fields Inst. Commun. 38, 223--231 (2003; Zbl 1062.11038)] conjectured a number of supercongruences for hypergeometric Calabi-Yau manifolds of dimension \(d\leq 3\). For manifolds of dimension \(d=1\), he observed four potential supercongruences. Later that author proved one of the four. Motivated by Rodriguez-Villegas's work, in the paper under review the present author proves a general result on supercongruences between values of truncated \(_{2}F_{1}\) hypergeometric functions and Gaussian hypergeometric functions. As a corollary to that result, he proves the three remaining supercongruences.
- University of Queensland Australia
- University of Wisconsin System United States
- University of Queensland Australia
- University of Wisconsin–Madison United States
- University of Wisconsin–Oshkosh United States
Curves over finite and local fields, Classical hypergeometric functions, \({}_2F_1\), 0199 Other Mathematical Sciences, Congruences; primitive roots; residue systems, Manifolds, Gaussian hypergeometic functions, Jacobsthal and Brewer sums; other complete character sums, supercongruences, 01 Mathematical Sciences
Curves over finite and local fields, Classical hypergeometric functions, \({}_2F_1\), 0199 Other Mathematical Sciences, Congruences; primitive roots; residue systems, Manifolds, Gaussian hypergeometic functions, Jacobsthal and Brewer sums; other complete character sums, supercongruences, 01 Mathematical Sciences
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