A supercongruence conjecture of Rodriguez-Villegas for a certain truncated hypergeometric function

Mortenson, Eric (2003) A supercongruence conjecture of Rodriguez-Villegas for a certain truncated hypergeometric function. Journal of Number Theory, 99 1: 139-147. doi:10.1016/S0022-314X(02)00052-5


Author Mortenson, Eric
Title A supercongruence conjecture of Rodriguez-Villegas for a certain truncated hypergeometric function
Journal name Journal of Number Theory   Check publisher's open access policy
ISSN 0022-314X
1096-1658
Publication date 2003-03
Sub-type Article (original research)
DOI 10.1016/S0022-314X(02)00052-5
Volume 99
Issue 1
Start page 139
End page 147
Total pages 9
Publisher Academic Press
Language eng
Subject 01 Mathematical Sciences
Abstract Fernando Rodriguez-Villegas has been studying hypergeometric families of Calabi–Yau manifolds, and from his investigations he has found (numerically) many possible supercongruences. For example, he conjectures for every odd prime p that Image Here, we use the theory of Gaussian hypergeometric series, the properties of the p-adic Γ-function, and a strange combinatorial identity to prove this conjecture.
Keyword Supercongruences
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collections: Excellence in Research Australia (ERA) - Collection
School of Mathematics and Physics
 
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