{"paper":{"title":"Solutions modulo $p$ of Gauss-Manin differential equations for multidimensional hypergeometric integrals and associated Bethe ansatz","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.NT","math.QA"],"primary_cat":"math.AG","authors_text":"Alexander Varchenko","submitted_at":"2017-09-18T22:16:51Z","abstract_excerpt":"We consider the Gauss-Manin differential equations for hypergeometric integrals associated with a family of weighted arrangements of hyperplanes moving parallelly to themselves. We reduce these equations modulo a prime integer $p$ and construct polynomial solutions of the new differential equations as $p$-analogs of the initial hypergeometric integrals.\n  In some cases we interpret the $p$-analogs of the hypergeometric integrals as sums over points of hypersurfaces defined over the finite field $F_p$. That interpretation is similar to the interpretation by Yu.I. Manin in [Ma] of the number of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06189","kind":"arxiv","version":2},"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"}