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Establishing inequalities of this variety is motiv"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1006.4323","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-06-22T16:30:18Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"4ad19cb4b5fa795a2dc63f43ddb2d880255228032107816b383dd47719ac31b8","abstract_canon_sha256":"6ae0d564f4336697f1a98d4b6147766529e9afdd4f3de72ca482c5422264e811"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:13.957828Z","signature_b64":"0SmtNch3kvVirsJe+p0mrkTF0e72ap6sFdhWnK4YwSIVJQfgCHrf0u36RkTWCFAIvPV0jc67YgojdrcHdpoZAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4ffae01afd7f178983a433d3fa3350f61c802eaefd9cf060371268f7c214fb3","last_reissued_at":"2026-05-18T04:41:13.957340Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:13.957340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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