Related papers: Some Numeric Hypergeometric Supercongruences
In this article we derive both Hamilton type and Souplet-Zhang type gradient estimations for a system of semilinear equations along a geometric flow on a weighted Riemannian manifold.
This paper explores the calculus of dual-valued functions and investigates the gamma function, beta function and generalized hypergeometric functions by incorporating dual numbers as parameters and variables. We examine its fundamental…
In this paper, based on the toric hypergeometric model given in a paper by Beukers--Cohen--Mellit, we provide two other ways to explain why the zig-zag diagram method can be used to compute Hodge numbers for hypergeometric data defined over…
The geometry of (2,1) supersymmetric sigma-models with isometry symmetries is discussed. The gauging of such symmetries in superspace is then studied. We find that the coupling to the (2,1) Yang-Mills supermultiplet can be achieved provided…
Rodriguez-Villegas conjectured four supercongruences associated to certain elliptic curves, which were first confirmed by Mortenson by using the Gross-Koblitz formula. In this paper, we aim to prove four supercongruences between two…
We elaborate on the expansion of hypergeometric functions about rational parameters, where we focus mainly on the integer and half-integer case. The strategy and the basic steps of a recently developed algorithm for the expansion about…
New duality transformation formulas are proposed for multiple elliptic hypergeometric series of type $BC$ and of type $C$. Various transformation and summation formulas are derived as special cases to recover some previously known results.
We construct rigid supersymmetric gauge theories on Riemannian five-manifolds. We follow a holographic approach, realizing the manifold as the conformal boundary of a six-dimensional bulk supergravity solution. This leads to a systematic…
In a recent article, Apagodu and Zeilberger (http://arxiv.org/abs/1606.03351)discuss some applications of an algorithm for finding and proving congruence identities (modulo primes) of indefinite sums of many combinatorial sequence. At the…
We obtain new inequalities for certain hypergeometric functions. Using these inequalities, we deduce estimates for the hyperbolic metric and the induced distance function on a certain canonical hyperbolic plane domain.
Recently, many researchers devoted their attention to study the extensions of the gamma and beta functions. In the present work, we focus on investigating some approximations for a class of Gauss hypergeometric functions by exploiting…
In this short paper we propose four conjectures in synthetic geometry that generalize Erdos-Mordell Theorem, and three conjectures in number theory that generalize Fermat Numbers.
We construct explicitly classical and quantum supercharges satisfying the standard N = 4 supersymmetry algebra in the supersymmetric sigma models describing the motion over HKT (hyper-Kaehler with torsion) manifolds. One member of the…
In the paper, the author finds an explicit formula for computing Bell numbers in terms of Kummer confluent hypergeometric functions and Stirling numbers of the second kind.
In terms of several summation and transformation formulas for basic hypergeometric series, two forms of the Chinese remainder theorem for coprime polynomials, the creative microscoping method introduced by Guo and Zudilin, Guo and Li's…
We discuss the gauge natural formulation of supersymmetric theories and supergravity, with the aim to show that the standard and the supersymmetric frameworks admit in fact a unifying mathematical language.
Multiple elliptic polylogarithms can be written as (multiple) integrals of products of basic hypergeometric functions. The latter are computable, to arbitrary precision, using a q-difference equation and q-contiguous relations.
In this note we will review the most important results and questions related to Chern conjecture and isoparametric hypersurfaces, as well as their interactions and applications to various aspects in mathematics.
In this paper, we present a new method for finding identities for hypergeoemtric series, such as the (Gauss) hypergeometric series, the generalized hypergeometric series and the Appell-Lauricella hypergeometric series. Furthermore, using…
In this paper, we obtain recursion formulas for the Kamp\'e de Fe\'riet hypergeometric matrix function. We also give finite and infinite summation formulas for the Kamp\'e de Fe\'riet hypergeometric matrix function.