{"paper":{"title":"An improved constant in Banaszczyk's transference theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.MG","authors_text":"Divesh Aggarwal, Noah Stephens-Davidowitz","submitted_at":"2019-07-21T19:35:07Z","abstract_excerpt":"$ \\newcommand{\\R}{\\ensuremath{\\mathbb{R}}} \\newcommand{\\lat}{\\mathcal{L}} \\newcommand{\\ensuremath}[1]{#1} $We show that \\[ \\mu(\\lat) \\lambda_1(\\lat^*) < \\big( 0.1275 + o(1) \\big) \\cdot n \\; , \\] where $\\mu(\\lat)$ is the covering radius of an $n$-dimensional lattice $\\lat \\subset \\R^n$ and $\\lambda_1(\\lat^*)$ is the length of the shortest non-zero vector in the dual lattice $\\lat^*$. This improves on Banaszczyk's celebrated transference theorem (Math. Annal., 1993) by about 20%.\n  Our proof follows Banaszczyk exactly, except in one step, where we replace a Fourier-analytic bound on the discrete"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09020","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"}