{"id":"https://openalex.org/W7214955966","doi":"https://doi.org/10.48550/arxiv.2609.37332","title":"Truncated pretentious distances of multiplicative arithmetic functions","display_name":"Truncated pretentious distances of multiplicative arithmetic functions","publication_year":2026,"publication_date":"2026-09-29","ids":{"openalex":"https://openalex.org/W7214955966","doi":"https://doi.org/10.48550/arxiv.2609.37332"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.37332","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37332","pdf_url":"https://arxiv.org/pdf/2609.37332","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":null,"license_id":null,"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/2609.37332","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5153641653","display_name":"Thomas Renard","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Renard, Thomas","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5153641653"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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":1.0,"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":1.0,"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":0.0,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.8109999895095825},{"id":"https://openalex.org/keywords/prime-numbers","display_name":"prime numbers","score":0.6029999852180481}],"concepts":[{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.8791000247001648},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8399999737739563},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6169999837875366},{"id":"https://openalex.org/C112343008","wikidata":"https://www.wikidata.org/wiki/Q140744","display_name":"Arithmetic function","level":2,"score":0.5825999975204468},{"id":"https://openalex.org/C5297727","wikidata":"https://www.wikidata.org/wiki/Q786970","display_name":"Autocorrelation","level":2,"score":0.5669999718666077},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5583000183105469},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.47679999470710754},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.47600001096725464},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4350000023841858},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.42829999327659607},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3840000033378601},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.36340001225471497},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3215999901294708},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.30250000953674316},{"id":"https://openalex.org/C38803922","wikidata":"https://www.wikidata.org/wiki/Q95745348","display_name":"Additive function","level":2,"score":0.2962999939918518},{"id":"https://openalex.org/C157351203","wikidata":"https://www.wikidata.org/wiki/Q216906","display_name":"Multiplicative inverse","level":3,"score":0.2928999960422516},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.2915000021457672},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.27000001072883606},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.26759999990463257},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2549000084400177}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.37332","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37332","pdf_url":"https://arxiv.org/pdf/2609.37332","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.37332","doi":"https://doi.org/10.48550/arxiv.2609.37332","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.37332","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.37332","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.37332","pdf_url":"https://arxiv.org/pdf/2609.37332","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":null,"license_id":null,"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/W7214955966.pdf","grobid_xml":"https://content.openalex.org/works/W7214955966.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1557923169","https://openalex.org/W2742251634","https://openalex.org/W2890529019","https://openalex.org/W2962959302","https://openalex.org/W4365211780"],"related_works":["https://openalex.org/W7172075976","https://openalex.org/W2328627644","https://openalex.org/W1534531546","https://openalex.org/W4404360686","https://openalex.org/W4417088432","https://openalex.org/W2890529019","https://openalex.org/W2141281212","https://openalex.org/W2317507837","https://openalex.org/W2742251634","https://openalex.org/W4387956979"],"abstract_inverted_index":{"Let":[0],"$f\\colon\\mathbb{N}\\to\\mathbb{U}$":[1],"be":[2],"a":[3,56,74],"non-pretentious":[4,59],"multiplicative":[5,60],"function":[6],"in":[7,66],"the":[8,16,19,28,31,40,49],"sense":[9],"of":[10,18,22,35,39,58],"Granville":[11],"and":[12,43,79],"Soundararajan.":[13],"We":[14],"study":[15],"convergence":[17],"autocorrelation":[20],"averages":[21],"$f$.":[23],"In":[24],"particular,":[25],"we":[26,54],"investigate":[27],"relationship":[29],"between":[30],"local":[32],"pretentious":[33],"behaviour":[34],"$f$":[36],"on":[37,48,73],"intervals":[38],"form":[41],"$[x^{\\varepsilon},x]$":[42],"its":[44,67],"deviation":[45],"from":[46],"$1$":[47],"primes.":[50],"As":[51],"an":[52],"application,":[53],"exhibit":[55],"class":[57],"functions":[61],"for":[62],"which":[63],"Elliott's":[64],"conjecture":[65],"original":[68],"formulation":[69],"holds,":[70],"following":[71],"up":[72],"result":[75],"by":[76],"Klurman,":[77],"Mangerel":[78],"Ter\u00e4v\u00e4inen.":[80]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-01T00:00:00"}