{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T08:12:20Z","timestamp":1780560740530,"version":"3.54.1"},"reference-count":17,"publisher":"EDP Sciences","license":[{"start":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T00:00:00Z","timestamp":1780531200000},"content-version":"vor","delay-in-days":154,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12171286"],"award-info":[{"award-number":["12171286"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12571006"],"award-info":[{"award-number":["12571006"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Theor. Inf. Appl."],"accepted":{"date-parts":[[2026,4,29]]},"published-print":{"date-parts":[[2026]]},"abstract":"\n Let \u0394\n 2<\/jats:sub>\n (\n x<\/jats:italic>\n ) denote the error term in the asymptotic formula for the summatory function of\n d<\/jats:italic>\n (\n n<\/jats:italic>\n ). Let \u0394\n 1<\/jats:sub>\n (\n x<\/jats:italic>\n ; \u03c6) denote the error term in the asymptotic formula of the Riesz mean. This paper devoted to the study of the hybrid moments of \u0394\n 2<\/jats:sub>\n (\n x<\/jats:italic>\n ) and \u0394\n 1<\/jats:sub>\n (\n x<\/jats:italic>\n ; \u03c6).\n <\/jats:p>","DOI":"10.1051\/ita\/2026018","type":"journal-article","created":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T07:55:39Z","timestamp":1780559739000},"page":"18","source":"Crossref","is-referenced-by-count":0,"title":["On hybrid moments of \u0394\n 2<\/sub>\n (\n x<\/i>\n ) and \u0394\n 1<\/sub>\n (\n x<\/i>\n ; \u03c6)"],"prefix":"10.1051","volume":"60","author":[{"given":"Qian","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Shandong Normal University","place":["PR China"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jing","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shandong Normal University","place":["PR China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"250","published-online":{"date-parts":[[2026,6,4]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1051\/ita\/2026006","volume":"60","author":"Guo","year":"2026","journal-title":"RAIRO-Theor. Inf. Appl."},{"key":"R2","first-page":"1453","volume":"36","author":"Wu","year":"2025","journal-title":"Indag. Math.-New Ser."},{"key":"R3","unstructured":"Bourgain J. and Watt N., Mean square of zeta function, circle problem and divisor problem revisited. preprint arXiv:1709.04340."},{"key":"R4","first-page":"515","volume":"6","author":"Tong","year":"1956","journal-title":"Acta Math. Sin. Chinese Ser."},{"key":"R5","unstructured":"Ivi\u0107 A., The Riemann Zeta-Function. Wiley, New York (1985)."},{"key":"R6","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1112\/plms\/s3-65.1.65","volume":"65","author":"Tsang","year":"1992","journal-title":"Proc. London Math. 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A Math."},{"key":"R12","first-page":"795","volume":"46","author":"Huang","year":"2025","journal-title":"Front. Math."},{"key":"R13","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1007\/s11401-025-0036-x","volume":"46","author":"Huang","year":"2025","journal-title":"Chin. Ann. Math. Ser. B"},{"key":"R14","first-page":"329","volume":"115","author":"Robert","year":"2008","journal-title":"Acta Arith."},{"key":"R15","unstructured":"Kolesnik G., On the estimation of multiple exponential sums, in Recent Progress in Analytic Number Theory, Vol. 1 (Durham, 1979). Academic Press, London-New York (1981) 231\u2013246."},{"key":"R16","unstructured":"Kong K.L., Some Mean Value Theorems for Certain Error Terms in Analytic Number Theory. The University of Hong Kong (2014)."},{"key":"R17","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1007\/s11139-021-00431-w","volume":"58","author":"Cao","year":"2022","journal-title":"Ramanujan J."}],"container-title":["RAIRO - Theoretical Informatics and Applications"],"original-title":[],"link":[{"URL":"https:\/\/www.rairo-ita.org\/10.1051\/ita\/2026018\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T07:55:49Z","timestamp":1780559749000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.rairo-ita.org\/10.1051\/ita\/2026018"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026]]},"references-count":17,"alternative-id":["ita20260031"],"URL":"https:\/\/doi.org\/10.1051\/ita\/2026018","relation":{},"ISSN":["0988-3754","2804-7346"],"issn-type":[{"value":"0988-3754","type":"print"},{"value":"2804-7346","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026]]}}}