Related papers: Transformations of Hypergeometric Motives
Let X be an affine real algebraic set . We investigate on the theory of algebraically constructible functions on X and the description of the semi-algebraic subsets of X when we replace the polynomial functions on X by some rational…
Many product formulas are known classically for generalized hypergeometric functions over the complex numbers. In this paper, we establish some analogous formulas for generalized hypergeometric functions over finite fields.
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.
We investigate graph hypersurfaces and study conditions under which graph hypersurfaces admit algebraic torus operations. This leads in principle to a computation of graph motives using the theorem of Bialynicki-Birula, provided one knows…
The umbral approach provides methods for comprehending and redefining special functions. This approach is employed efficiently in order to uncover intricacies and introduce new families of special functions. In this article, the umbral…
We express explicitly the Heckman-Opdam hypergeometric function for the root system of type A with a certain degenerate parameter in terms of the Lauricella hypergeometric function.
In this paper, we first introduce certain forms of extended incomplete Pochhammer symbols which are then used to define families of extended incomplete generalized hypergeometric functions. For these functions, we investigate various…
We study the incomplete Mellin transformation of the fractional part and the related log-sine function when composed by an affine complex map. We evaluate the corresponding integral in two different ways which yields equalities with series…
We examine three-dimensional metric deformations based on a tetrad transformation through the action the matrices of scalar fields. We describe by this approach to deformation the results obtained by Coll et al. in [1], where it is stated…
Using the framework relating hypergeometric motives to modular forms, we define an explicit family of weight 2 Hecke eigenforms with complex multiplication. We use the theory of ${}_2F_1(1)$ hypergeometric series and Ramanujan's theory of…
In this paper we study hypergraphs definable in an algebraically closed field. Our goal is to show, in the spirit of the so-called transference principles in extremal combinatorics, that if a given algebraic hypergraph is "dense" in a…
There are many instances known when the Fourier coefficients of modular forms are congruent to partial sums of hypergeometric series. In our previous work arXiv:1803.01830, such partial sums are related to the radial asymptotics of infinite…
We survey some recent developments at the interface of algebraic geometry, surface topology, and the theory of ordinary differential equations. Motivated by "non-abelian" analogues of standard conjectures on the cohomology of algebraic…
We provide a complete classification of the algebraicity of (generalized) hypergeometric functions with no restriction on the set of their parameters. Our characterization relies on the interlacing criteria of Christol (1987) and…
We give a new method to prove in a uniform and easy way various transformation formulas for Gauss hypergeometric functions. The key is Jacobi's canonical form of the hypergeometric differential equation. Analogy for $q$-hypergeometric…
A hyperbolic algebraic curve is a bounded subset of an algebraic set. We study the function theory and functional analytic aspects of these sets. We show that their function theory can be described by finite codimensional subalgebras of the…
We prove a transformation formula relating two determinants involving elliptic shifted factorials. Similar determinants have been applied to multiple elliptic hypergeometric series.
We combine several mini miracles to achieve an elementary understanding of infinite loop spaces and very effective spectra in the algebro-geometric setting of motivic homotopy theory. Our approach combines $\Gamma$-spaces and framed…
The goal of inversion is to estimate the model which generates the data of observations with a specific modeling equation. One general approach to inversion is to use optimization methods which are algebraic in nature to define an objective…
The purpose of these notes is to give a short survey of an interesting connection between partition functions of supersymmetric gauge theories and hypergeometric functions and to present the recent progress in this direction.