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The method of proof shows that the absolute constant $A$ in the inequality \\[ \\sup_{1\\le n_1<\\cdots < n_N} \\sum_{k,{\\ell}=1}^N\\frac{\\gcd(n_k,n_{\\ell})}{\\sqrt{n_k n_{\\ell}}} \\ll N \\exp\\left(A\\sqrt{\\frac{\\log N \\log\\log\\log N}{\\log\\log N}}\\right), \\] established in a recent paper of ours, cannot be taken smaller than $1$."},"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":"1507.05840","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-07-21T14:12:12Z","cross_cats_sorted":[],"title_canon_sha256":"d5743a5955c2b7f82cf93f4112c20cab31aec6b59b657c066fa8085249b38787","abstract_canon_sha256":"ac742749e999ea3375b5b256788c75777e77dd79c2e6a7673d9a2124fc5bb81e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:44.975770Z","signature_b64":"RJP/9/TaWQdRxIaAgz1j59A9f4houEd61mJWqflEz1X2zCYGRAqAA+mSuiY/MhBkOsWy7fiZboqDbUUcJaJ5Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc8c0562eb40d68251332a71dbfe19f2c5328c817f949d5300251f7790cd417a","last_reissued_at":"2026-05-18T00:32:44.975081Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:44.975081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large GCD sums and extreme values of the Riemann zeta function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andriy Bondarenko, Kristian Seip","submitted_at":"2015-07-21T14:12:12Z","abstract_excerpt":"It is shown that the maximum of $|\\zeta(1/2+it)|$ on the interval $T^{1/2}\\le t \\le T$ is at least $\\exp\\left((1/\\sqrt{2}+o(1)) \\sqrt{\\log T \\log\\log\\log T/\\log\\log T}\\right)$. Our proof uses Soundararajan's resonance method and a certain large GCD sum. 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