{"id":"https://openalex.org/W7204584707","doi":"https://doi.org/10.48550/arxiv.2608.26814","title":"Two-point correlations of multiplicative functions with dense orbits","display_name":"Two-point correlations of multiplicative functions with dense orbits","publication_year":2026,"publication_date":"2026-08-27","ids":{"openalex":"https://openalex.org/W7204584707","doi":"https://doi.org/10.48550/arxiv.2608.26814"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.26814","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.26814","pdf_url":"https://arxiv.org/pdf/2608.26814","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.26814","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5148551743","display_name":"N\u00e9o Tardy","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tardy, N\u00e9o","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5148551743"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.00019999999494757503,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/multiplicative-functions","display_name":"multiplicative functions","score":0.8429999947547913},{"id":"https://openalex.org/keywords/completely-multiplicative-functions","display_name":"completely multiplicative functions","score":0.8489999771118164},{"id":"https://openalex.org/keywords/two-point-correlation-function","display_name":"two-point correlation function","score":0.8759999871253967},{"id":"https://openalex.org/keywords/dense-orbits","display_name":"dense orbits","score":0.9070000052452087},{"id":"https://openalex.org/keywords/multiplicative-number-theory","display_name":"multiplicative number theory","score":0.4790000021457672},{"id":"https://openalex.org/keywords/uniform-distribution-modulo-1","display_name":"uniform distribution modulo one","score":0.5139999985694885}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7491000294685364},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.7254999876022339},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.7250000238418579},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5358999967575073},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5303000211715698},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39969998598098755},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.37950000166893005},{"id":"https://openalex.org/C42357961","wikidata":"https://www.wikidata.org/wiki/Q213363","display_name":"Open set","level":2,"score":0.34549999237060547},{"id":"https://openalex.org/C2984157986","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Periodic orbits","level":2,"score":0.33500000834465027},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3239000141620636},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3041999936103821},{"id":"https://openalex.org/C7356347","wikidata":"https://www.wikidata.org/wiki/Q1307838","display_name":"Unit square","level":2,"score":0.28279998898506165},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.27639999985694885},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.27070000767707825},{"id":"https://openalex.org/C47177299","wikidata":"https://www.wikidata.org/wiki/Q2390323","display_name":"Unit disk","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.25679999589920044},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.25619998574256897}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.26814","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.26814","pdf_url":"https://arxiv.org/pdf/2608.26814","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.26814","doi":"https://doi.org/10.48550/arxiv.2608.26814","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.26814","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.26814","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.26814","pdf_url":"https://arxiv.org/pdf/2608.26814","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204584707.pdf","grobid_xml":"https://content.openalex.org/works/W7204584707.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W4365211780","https://openalex.org/W4403752126"],"related_works":["https://openalex.org/W2896422964","https://openalex.org/W4381252824","https://openalex.org/W3035093900","https://openalex.org/W2063429167","https://openalex.org/W4410212937","https://openalex.org/W4365211780","https://openalex.org/W2761612058","https://openalex.org/W4213011916","https://openalex.org/W2433127072","https://openalex.org/W2890529019"],"abstract_inverted_index":{"Let":[0],"$f,g:\\mathbb{N}\\to\\mathbb{T}$":[1],"be":[2],"completely":[3],"multiplicative":[4],"functions":[5],"with":[6],"dense":[7],"images":[8],"in":[9],"the":[10,26,42],"complex":[11],"unit":[12],"circle":[13],"$\\mathbb{T}$.":[14],"We":[15],"prove":[16],"that,":[17],"for":[18],"every":[19],"non-empty":[20],"open":[21],"set":[22,27],"$U":[23],"\\subset":[24],"\\mathbb{T}^2$,":[25],"of":[28,46,55,62],"integers":[29],"$n$":[30],"such":[31],"that":[32],"$(f(n),g(n+1))":[33],"\\in":[34],"U$":[35],"has":[36],"positive":[37],"upper":[38],"logarithmic":[39],"density,":[40],"unless":[41],"pair":[43],"$(f,g)$":[44],"is":[45],"a":[47],"special":[48],"form.":[49],"This":[50],"result":[51],"strengthens":[52],"earlier":[53],"theorems":[54],"Klurman":[56],"and":[57,65,67],"Mangerel,":[58],"as":[59,61],"well":[60],"Charamaras,":[63],"Mountakis,":[64],"Tsinas,":[66],"yields":[68],"simpler":[69],"proofs.":[70]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-08-29T00:00:00"}