{"paper":{"title":"Gauss congruences for rational functions in several variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Armin Straub, Frits Beukers, Marc Houben","submitted_at":"2017-10-01T21:57:26Z","abstract_excerpt":"We investigate necessary as well as sufficient conditions under which the Laurent series coefficients $f_{\\boldsymbol{n}}$ associated to a multivariate rational function satisfy Gauss congruences, that is $f_{\\boldsymbol{m}p^r} \\equiv f_{\\boldsymbol{m}p^{r-1}}$ modulo $p^r$. For instance, we show that these congruences hold for certain determinants of logarithmic derivatives. As an application, we completely classify rational functions $P/Q$ satisfying the Gauss congruences in the case that $Q$ is linear in each variable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00423","kind":"arxiv","version":1},"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"}