Gevrey and formal Nilsson solutions of $A$-hypergeometric systems

Abstract

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 some additional conditions, both spaces are equal. In the process we prove some other results about formal Nilsson solutions.

14 pages, 1 figure. Section 3 has been improved. In particular, new Theorem 3.3 and Theorem 3.4 replace Theorem 3.2 and Corollary 3.4 in the previous version, and we don't need now any condition on the parameters, except for the computation of the dimension of Gevrey series solutions of the hypergeometric system