{"paper":{"title":"The size of exponential sums on intervals of the real line","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"math.CA","authors_text":"Kaveh Khodjasteh, Lorenza Viola, Tam\\'as Erd\\'elyi","submitted_at":"2010-06-22T16:30:18Z","abstract_excerpt":"We prove that there is a constant $c > 0$ depending only on $M \\geq 1$ and $\\mu \\geq 0$ such that $$\\int_y^{y+a}{|g(t)| \\, dt} \\geq \\exp (-c/(a\\delta))\\,, a \\in (0,\\pi]\\,,$$ for every $g$ of the form $$g(t) = \\sum_{j=0}^n{a_j e^{i\\lambda_jt}}, a_j \\in {\\Bbb C}, \\enskip |a_j| \\leq Mj^\\mu\\,, \\enskip |a_0|=1\\,, \\enskip n \\in {\\Bbb N} \\,,$$ where the exponents $\\lambda_j \\in {\\Bbb C}$ satisfy $$\\text{\\rm Re}(\\lambda_0) = 0\\,, \\qquad \\text{\\rm Re}(\\lambda_j) \\geq j\\delta > 0\\,, j=1,2,\\ldots\\,,$$ and for every subinterval $[y,y+a]$ of the real line. Establishing inequalities of this variety is motiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.4323","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"}