Abstract
We prove that a holonomic binomial D-module M A (I, β) is regular if and only if certain associated primes of I determined by the parameter vector $${\beta\in \mathbb{C}^d}$$ are homogeneous. We further describe the slopes of M A (I, β) along a coordinate subspace in terms of the known slopes of some related hypergeometric D-modules that also depend on β. When the parameter β is generic, we also compute the dimension of the generic stalk of the irregularity of M A (I, β) along a coordinate hyperplane and provide some remarks about the construction of its Gevrey solutions.
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