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Several upper bounds for integrals of the type $$ \\int_0^T\\Delta^k(t)|\\zeta(1/2+it)|^{2m}dt \\qquad(k,m\\in\\Bbb N) $$ are given. This complements the results of the paper Ivi\\'c-Zhai [Indag. Math. 2015], where asymptotic formulas for $2\\le k \\le 8,m =1$ were established for the above integral."},"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":"1508.06394","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-08-26T07:50:10Z","cross_cats_sorted":[],"title_canon_sha256":"93a4b894700f405f0c844ae308c1019d856ea85ffb758633bc41bd793aa1f720","abstract_canon_sha256":"bf7c39977b447f4d5d8425cc2beac3cfb16ff505b13948141636e7ccaaf2b8b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:55.495253Z","signature_b64":"WGJC8yeaK9xoKQMmcs981K6p8ZfWUsTrhvJZWKDTjcS1YNS5lkEg248Fj6dCujMDleR1PIZ7A8ZQIPXVpOG5Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8bfa5007c74165a2b8828deb5d6675b7e86aa941a94c9b80839bc3cadc305b45","last_reissued_at":"2026-05-18T00:58:55.494602Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:55.494602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On some upper bounds for the zeta-function and the Dirichlet divisor problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Aleksandar Ivi\\'c","submitted_at":"2015-08-26T07:50:10Z","abstract_excerpt":"Let $d(n)$ be the number of divisors of $n$, let $$ \\Delta(x) := \\sum_{n\\le x}d(n) - x(\\log x + 2\\gamma -1) $$ denote the error term in the classical Dirichlet divisor problem, and let $\\zeta(s)$ denote the Riemann zeta-function. 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