On the $b$-functions of hypergeometric systems

Thomas Reichelt; Christian Sevenheck; Uli Walther

On the $b$-functions of hypergeometric systems

Algebraic Geometry 2017-02-13 v3

Authors: Thomas Reichelt , Christian Sevenheck , Uli Walther

Abstract

For any integer $d\times (n+1)$ matrix $A$ and parameter $\beta\in\CC^d$ 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.

Keywords

hypergeometric functions random matrix ensembles zeta functions

Cite

@article{arxiv.1511.03327,
  title  = {On the $b$-functions of hypergeometric systems},
  author = {Thomas Reichelt and Christian Sevenheck and Uli Walther},
  journal= {arXiv preprint arXiv:1511.03327},
  year   = {2017}
}

Comments

14 pages, several figures. Typos corrected

On the $b$-functions of hypergeometric systems

Abstract

Keywords

Cite

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