Related papers: Gevrey solutions for irregular hypergeometric syst…
We describe the Gevrey series solutions at singular points of the irregular hypergeometric system (GKZ system) associated with an affine plane monomial curve. We also describe the irregularity complex of such a system with respect to its…
We describe the Gevrey series solutions at singular points of the irregular hypergeometric system (GKZ system) associated with an affine monomial curve. We also describe the irregularity complex of such a system with respect to its singular…
We study integral representations of the Gevrey series solutions of irregular hypergeometric systems under certain assumptions. We prove that, for such systems, any Gevrey series solution, along a coordinate hyperplane of its singular…
We study integral representations of the Gevrey series solutions of irregular hypergeometric systems. In this paper we consider the case of the systems associated with a one row matrix, for which the integration domains are one dimensional.…
We compute, by D-module restrictions, the slopes of irregular hypergeometric systems associated to a monomial curve.
We make a detailed analysis of the A-hypergeometric system (or GKZ system) associated with a monomial curve and integral, hence resonant, exponents. We characterize the Laurent polynomial solutions and show that these are the only rational…
We will introduce a modified system of A-hypergeometric system (GKZ system) by applying a change of variables for Groebner deformations and study its Groebner basis and the indicial polynomials along the "exceptional hypersurface".
A modified $A$-hypergeometric system is a system of differential equations for the function $f(t^w \cdot x)$ where $f(y)$ is a solution of an $A$-hypergeometric system in $n$ variables and $w$ is an $n$ dimensional integer vector, which is…
The GKZ system for the Hesse pencil of elliptic curves has more solutions than the period integrals. In this work we give different realizations and interpretations of the extra solution, in terms of oscillating integral, Eichler integral,…
We consider Mellin-Barnes integral representations of GKZ hypergeometric equations. We construct integration contours in an explicit way and show that suitable analytic continuations give rise to a basis of solutions.
For a finite set A of integral vectors, Gel'fand, Kapranov and Zelevinskii defined a system of differential equations with a parameter vector as a D-module, which system is called an A-hypergeometric (or a GKZ hypergeometric) system.…
We introduce a hypergoemetirc series with two complex variables, which generalizes Appell's, Lauricella's and Kemp\'e de F\'eriet's hypergeometric series, and study the system of differential equations that it satisfies. We determine the…
We analyze GKZ(Gel'fand, Kapranov and Zelevinski) hypergeometric systems and apply them to study the quantum cohomology rings of Calabi-Yau manifolds. We will relate properties of the local solutions near the large radius limit to the…
We study Feynman integrals in the framework of Gel'fand-Kapranov-Zelevinsky (GKZ) hypergeometric systems. The latter defines a class of functions wherein Feynman integrals arise as special cases, for any number of loops and kinematic…
We discuss some research problems on affine monomial curves, from the perspective of computation.
We produce a decomposition of the parameter space of the $A$-hypergeometric system associated to a projective monomial curve as a union of an arrangement of lines and its complement, in such a way that the analytic behavior of the solutions…
In this paper, we study the Gevrey regularity of weak solution for a class of linear and quasilinear Fokker-Planck equations.
The goal of this paper is to investigate Gevrey properties of formal solutions of certain generalized linear partial differential equations with variable coefficients. In particular, we extend the notion of moment partial differential…
Our aim in this paper is to prove, under some growth conditions on the datas, the solvability in a Gevrey class of a polynomially nonlinear functional differential equation.
Basing on Mellin-Barnes representations and Miller's transformation, we present the Gel'fand-Kapranov-Zelevinsky (GKZ) hypergeometric systems of 4-loop vacuum Feynman integrals with arbitrary masses. Through the GKZ hypergeometric systems,…