{"paper":{"title":"On the multivariate Fujiwara bound for exponential sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.MG"],"primary_cat":"math.AG","authors_text":"Jens Forsg{\\aa}rd","submitted_at":"2016-12-12T15:18:25Z","abstract_excerpt":"We prove the multivariate Fujiwara bound for exponential sums: for a $d$-variate exponential sum $f$ with scaling parameter $\\mu$, if $x$ is contained in the amoeba $\\mathscr{A}(f)$, then the distance from $x$ to the Archimedean tropical variety associated to $f$ is at most $d \\sqrt{d}\\, 2\\log(2 + \\sqrt{3})/ \\mu$. If $f$ is polynomial, then the bound can be improved to $d \\log(2 + \\sqrt{3})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03738","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"}