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On the \(b\)-functions of hypergeometric systems. (English) Zbl 1417.32007
Summary: For any integer \(d\times (n+1)\) matrix \(A\) and parameter \(\beta\in\mathbb C^d\) let \(M_A(\beta)\) be the associated \(A\)-hypergeometric (or GKZ) system in the variables \(x_0,\dots,x_n\). We describe bounds for the (roots of the) \(b\)-functions of both \(M_A(\beta)\) and its Fourier transform along the hyperplanes \((x_j=0)\). We also give an estimate for the \(b\)-function for restricting \(M_A(\beta)\) to a generic point.

MSC:
32C38 Sheaves of differential operators and their modules, \(D\)-modules
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