## 11 Citations

Hypergeometric Supercongruences

- Mathematics2017 MATRIX Annals
- 2019

We discuss two related principles for hypergeometric supercongrences, one related to accelerated convergence and the other to the vanishing of Hodge numbers. This is an extended abstract of a talk…

A Whipple $$_7F_6$$ Formula Revisited

- MathematicsLa Matematica
- 2022

A well-known formula of Whipple relates certain hypergeometric values $_7F_6(1)$ and $_4F_3(1)$. In this paper we revisit this relation from the viewpoint of the underlying hypergeometric data $HD$,…

Some supercongruences of arbitrary length

- Mathematics
- 2018

We prove supercongruences modulo $p^2$ for values of truncated hypergeometric series at some special points. The parameters of the hypergeometric series are $d$ copies of $1/2$ and $d$ copies of $1$…

Proof of some conjectural supercongruences of Guo and Schlosser

- Mathematics
- 2020

In this paper, we deduce certain supercongruence relations concerning truncated hypergeometric series. As particular cases, we confirm some recent conjectural supercongruences of Guo and Schlosser on…

$p$-adic analogues of hypergeometric identities

- Mathematics
- 2017

α(α+ 1) · · · (α+ k − 1), if k ≥ 1, 1, if k = 0. It is easy to see that (1.1) absolutely converges whenever |z| < 1, or |z| = 1 and R(β1 + · · ·+ βm) > R(α0+ · · ·+αm). If (1.1) is convergent, it is…

Some numeric hypergeometric
supercongruences

- Mathematics
- 2018

In this article, we list a few hypergeometric supercongruence conjectures based on two evaluation formulas of Whipple and numeric data computed using Magma and Sagemath.

Dwork-type supercongruences through a creative q-microscope

- MathematicsJ. Comb. Theory, Ser. A
- 2021

(q-)Supercongruences hit again

- Mathematics
- 2020

Using an intrinsic $q$-hypergeometric strategy, we generalise Dwork-type congruences $H(p^{s+1})/H(p^s)\equiv H(p^s)/H(p^{s-1})\pmod{p^3}$ for $s=1,2,\dots$ and $p$ a prime, when $H(N)$ are truncated…

## References

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GKZ-Generalized Hypergeometric Systems in Mirror Symmetry of Calabi-Yau Hypersurfaces

- Mathematics
- 1995

We present a detailed study of the generalized hypergeometric system introduced by Gel'fand, Kapranov and Zelevinski (GKZ-hypergeometric system) in the context of toric geometry. GKZ systems arise…

On the supercongruence conjectures of van Hamme

- Mathematics
- 2015

In 1997, van Hamme developed $$p$$p–adic analogs, for primes p, of several series which relate hypergeometric series to values of the gamma function, originally studied by Ramanujan. These analogs…

Computing the Level of a Modular Rigid Calabi-Yau Threefold

- MathematicsExp. Math.
- 2004

This work recalls a result of Serre giving a bound for the conductor of “integral” two-dimensional compatible families of Galois representations and applies this result to give an algorithm that determines the level of a modular rigid Calabi-Yau threefold.

On the modularity of rigid Calabi−Yau threefolds: epilogue

- Mathematics
- 2009

In a recent paper by F. Gouvea and N. Yui, a detailed account is given of a patching argument due to Serre that proves that the modularity of all rigid Calabi–Yau threefolds defined over $$…

The 14th case VHS via K3 fibrations

- Mathematics
- 2016

We present a study of certain singular one-parameter subfamilies of Calabi-Yau threefolds realized as anticanonical hypersurfaces or complete intersections in toric varieties. Our attention to these…

On a supercongruence conjecture of Rodriguez-Villegas

- Mathematics
- 2012

In examining the relationship between the number of points over $\mathbb{F}_p$ on certain Calabi-Yau manifolds and hypergeometric series which correspond to a particular period of the manifold,…

Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds

- Mathematics
- 2006

Abstract In this paper we are concerned with the monodromy of Picard-Fuchs differential equations associated with one-parameter families of Calabi-Yau threefolds. Our results show that in the…

Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties

- Mathematics
- 1993

We formulate general conjectures about the relationship between the A-model connection on the cohomology of ad-dimensional Calabi-Yau complete intersectionV ofr hypersurfacesV1,...,Vr in a toric…

Zeta functions of alternate mirror Calabi–Yau families

- MathematicsIsrael Journal of Mathematics
- 2018

We prove that if two Calabi–Yau invertible pencils have the same dual weights, then they share a common factor in their zeta functions. By using Dwork cohomology, we demonstrate that this common…