On the b-Functions of Hypergeometric Systems.

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 |$x_0,\ldots,x_n$|⁠. 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. [ABSTRACT FROM AUTHOR]