# zbMATH — the first resource for mathematics

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
##### Keywords:
$$D$$-modules; $$b$$-functions
Full Text: