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We also prove an exact inequality between the $L^p$-norm of a polynomial $P$ on $\\mathbb{T}^n$ and its Mahler measure $M(P)$, which is the geometric mean of $|P|$ with respect to the normalized Lebesgue m"},"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":"1508.05556","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-08-23T01:59:15Z","cross_cats_sorted":[],"title_canon_sha256":"6f0d0e5ab8971d1b419964068f9fa299fd552a6a7a35baaadaf98207753db793","abstract_canon_sha256":"469f4da5345e5d5812cff512ce380eacc652de7242883e7adde2b0093092770f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:52.207505Z","signature_b64":"Hxb0i1BKtMr16j5M/F1UcGyxA0J5+OW20Mh+qdYOyThKDTOChZxats0m5I+JEtzEWWjDV6rBLHXqWb+2mz2OCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e604d4a828ced298dc609f263365e35f95df24fe6233ac8b311c717c380a2ac8","last_reissued_at":"2026-05-18T01:34:52.206920Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:52.206920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$L^p$-norms and Mahler's measure of polynomials on the $n$-dimensional torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Andreas Defant, Mieczys{\\l}aw Masty{\\l}o","submitted_at":"2015-08-23T01:59:15Z","abstract_excerpt":"We prove Nikol'skii type inequalities which for polynomials on the $n$-dimensional torus $\\mathbb{T}^n$ relate the $L^p$-with the $L^q$-norm (with respect to the normalized Lebesgue measure and $0 <p <q < \\infty$). 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