{"paper":{"title":"On the $b$-functions of hypergeometric systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Christian Sevenheck, Thomas Reichelt, Uli Walther","submitted_at":"2015-11-10T22:51:13Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03327","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}