On theb-Functions of Hypergeometric Systems
Thomas Reichelt, Christian Sevenheck, Uli Walther · International Mathematics Research Notices · 2017
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.