{"paper":{"title":"Riesz Polarization Inequalities in Higher Dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.MP"],"primary_cat":"math-ph","authors_text":"Edward B. Saff, Tamas Erd\\'elyi","submitted_at":"2012-06-20T21:55:52Z","abstract_excerpt":"We derive bounds and asymptotics for the maximum Riesz polarization quantity $$M_n^p(A) := \\max_{{\\bold x}_1, {\\bold x}_2, \\ldots, {\\bold x}_n \\in A} {\\min_{{\\bold x} \\in A}{\\sum_{j=1}^n{\\frac{1}{|{\\bold x} - {\\bold x}_j|^{p}}}}}$$ (which is $n$ times the Chebyshev constant) for quite general sets $A \\subset {\\Bbb R}^m$ with special focus on the unit sphere and unit ball. We combine elementary averaging arguments with potential theoretic tools to formulate and prove our results. We also give a discrete version of the recent result of Hardin, Kendall, and Saff which solves the Riesz polarizatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4729","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"}