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In a recent paper we combined close to sharp upper bounds for the modulus of the autocorrelation coefficients of the Rudin-Shapiro polynomials with a deep theorem of Littlewood to prove that there is an absolute constant $A>0$ such that the equation $R_k(t) = (1+\\eta )n$ has at least $An^{0.5394282}$ distinct zeros in $[0,2\\pi)$ whenever $\\eta$ is real and $|\\eta| < 2^{-11}$. In this paper we show that the equation $R_k(t)=(1+\\eta)n$"},"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":"1802.02906","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CA","submitted_at":"2018-02-07T17:12:26Z","cross_cats_sorted":[],"title_canon_sha256":"d35e697d789382fdcec7acfd5167fad8d46550a0abc9e4ca93e1dfb39db741db","abstract_canon_sha256":"b48246e4ef6a801a61c1f6bb2d24b1048ec19126a63077096d9947f9710f9fa7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:14.287670Z","signature_b64":"fM4i7l8SuaCvf4+3r5GyDxYqXkQQACRRb6KwvgsAPtaow5RSkQcbw0NME1V2lXr4yjrJnAi1Ify591DeC/fzBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfbcc7cb1290276d0e6f24ab1017f6626245d6397c6f16b025708bc5c7a92f01","last_reissued_at":"2026-05-18T00:05:14.287175Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:14.287175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improved results on the oscillation of the modulus of the Rudin-Shapiro polynomials on the unit circle","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Tam\\'as Erd\\'elyi","submitted_at":"2018-02-07T17:12:26Z","abstract_excerpt":"Let either $R_k(t) := |P_k(e^{it})|^2$ or $R_k(t) := |Q_k(e^{it})|^2$, where $P_k$ and $Q_k$ are the usual Rudin-Shapiro polynomials of degree $n-1$ with $n=2^k$. In a recent paper we combined close to sharp upper bounds for the modulus of the autocorrelation coefficients of the Rudin-Shapiro polynomials with a deep theorem of Littlewood to prove that there is an absolute constant $A>0$ such that the equation $R_k(t) = (1+\\eta )n$ has at least $An^{0.5394282}$ distinct zeros in $[0,2\\pi)$ whenever $\\eta$ is real and $|\\eta| < 2^{-11}$. 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