We review some classical and modern aspects of hypergeometric differential equations,
including A-hypergeometric systems of Gel'′ fand, Graev, Kapranov and Zelevinsky. Some …

We study the irregularity of hypergeometric D-modules MA (β) via the explicit construction of
Gevrey series solutions along coordinate subspaces in X= Cn. As a consequence, we prove …

We study the solutions of irregular A-hypergeometric systems that are constructed from
Gröbner degenerations with respect to generic positive weight vectors. These are formal …

Let A be an integer matrix, and assume that its semigroup ring C [NA] is normal. Fix a face F
of the cone of A. We show that the projection and restriction of an A-hypergeometric system …

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 …

RESTRICTION OF HYPERGEOMETRIC 𝒟-MODULES WITH RESPECT TO COORDINATE
SUBSPACES Page 1 PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume …

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 …

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 …

We prove that a holonomic binomial D-module MA (I, β) is regular if and only if certain
associated primes of I determined by the parameter vector β ∈ C^ d are homogeneous. We …

We prove that the space of Gevrey solutions of an A–hypergeometric system along a
coordinate subspace is contained in a space of formal Nilsson solutions. Moreover, under …