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We prove $E(x)\\ll x^{1/2}(\\log x)^A(\\log\\log x)^4$with $A=3/2$ under the Generalized Riemann Hypothesis. This is a small improvement of the previous remarks of Mikawa (1993) and Perelli-Zaccagnini (1995) which claims $A=4,3$ respectively."},"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":"1504.04711","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-04-18T11:46:33Z","cross_cats_sorted":[],"title_canon_sha256":"cc7d391d42b5f1135fccc39e75cc6217ee5fa5c3676f389f4b4a6e673d99f361","abstract_canon_sha256":"4e40b0cb6019aa150d2d2be4d7a1e57bd5b2a5d1311b729174d3fd8296e94821"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:25.051897Z","signature_b64":"Aycfh5/PAs4eUeuYjebjspXlE8ufk1rmE92p3ez1SaM3mdffi+sEiNZzRCY/PONMbUzTld4QX+WkmR5iZZ/XBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b1a6708389a7dc4f082f9b52fd829eb799689913b83bc57d65cde5f42d6b9b7","last_reissued_at":"2026-05-18T02:18:25.051422Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:25.051422Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A remark on the conditional estimate for the sum of a prime and a square","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Yuta Suzuki","submitted_at":"2015-04-18T11:46:33Z","abstract_excerpt":"Hardy and Littlewood conjectured that every sufficiently large integer is either a square or the sum of a prime and a square. 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