On a supercongruence conjecture of Rodriguez-Villegas
Copyright policy )On a supercongruence conjecture of Rodriguez-Villegas
In examining the relationship between the number of points overFp\mathbb {F}_pon certain Calabi-Yau manifolds and hypergeometric series which correspond to a particular period of the manifold, Rodriguez-Villegas identified numerically 22 possible supercongruences. We prove one of the outstanding supercongruence conjectures between a special value of a truncated generalized hypergeometric series and thepp-th Fourier coefficient of a modular form.
- The University of Texas System United States
- Texas A&M University United States
Other character sums and Gauss sums, Generalized hypergeometric series, \({}_pF_q\), Mathematics - Number Theory, Calabi-Yau manifolds, FOS: Mathematics, supercongruence, Fourier coefficients, Number Theory (math.NT), Congruences for modular and \(p\)-adic modular forms, hypergeometric series
Other character sums and Gauss sums, Generalized hypergeometric series, \({}_pF_q\), Mathematics - Number Theory, Calabi-Yau manifolds, FOS: Mathematics, supercongruence, Fourier coefficients, Number Theory (math.NT), Congruences for modular and \(p\)-adic modular forms, hypergeometric series
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).33 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!