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We consider such polynomials for odd square-free n, where \\phi(n) coefficients are determined by the Jacobi symbol, but the remaining coefficients can be freely chosen. When n is prime, these polynomials have the smallest known asymptotic value of the normalised L_4 norm ||f||_4/||f||_2 among all Littlewood polynomials, namely (7/6)^{1/4}. When n is not prime, our results show that the normalised L_4 norm varies considerably accordin"},"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":"1105.5180","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-05-26T00:55:25Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"658574771a0e232cd58a9dce1975595cc9a067c370e2009b52c07b6375c5b432","abstract_canon_sha256":"2a930d53b67e19ac8174f9609ba7914760e5faa8473119795619be69ce951869"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:03.943551Z","signature_b64":"TRVBDfid6J/RXvRFaFVzuX//l8X4RclXhlHpR872Z1IkhyVFe94MVToQFqWaHGEiZn3uWUcj/4dlf9x0FsreAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d55775be829f5893cfdae7d9391fe1c5e31e6d792393f51443b752d7f656fb4","last_reissued_at":"2026-05-18T03:46:03.942851Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:03.942851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The L_4 norm of Littlewood polynomials derived from the Jacobi symbol","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.NT","authors_text":"Jonathan Jedwab, Kai-Uwe Schmidt","submitted_at":"2011-05-26T00:55:25Z","abstract_excerpt":"Littlewood raised the question of how slowly the L_4 norm ||f||_4 of a Littlewood polynomial f (having all coefficients in {-1,+1}) of degree n-1 can grow with n. 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