{"id":"https://openalex.org/W7214244175","doi":"https://doi.org/10.48550/arxiv.2609.28200","title":"On the hyperbolic prime number theorem","display_name":"On the hyperbolic prime number theorem","publication_year":2026,"publication_date":"2026-09-23","ids":{"openalex":"https://openalex.org/W7214244175","doi":"https://doi.org/10.48550/arxiv.2609.28200"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.28200","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.28200","pdf_url":"https://arxiv.org/pdf/2609.28200","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/2609.28200","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080101121","display_name":"Alisa Sedunova","orcid":"https://orcid.org/0000-0001-9972-3601","observed_orcids":["https://orcid.org/0000-0001-9972-3601"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Sedunova, Alisa","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5080101121"],"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":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/T11680","display_name":"Advanced Algebra and Geometry","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/upper-half-plane","display_name":"upper half-plane","score":0.722000002861023},{"id":"https://openalex.org/keywords/primes-in-arithmetic-progressions","display_name":"primes in arithmetic progressions","score":0.7369999885559082},{"id":"https://openalex.org/keywords/level-of-distribution","display_name":"level of distribution","score":0.8579999804496765},{"id":"https://openalex.org/keywords/sums-of-two-squares","display_name":"sums of two squares","score":0.7639999985694885},{"id":"https://openalex.org/keywords/asymptotic-formula","display_name":"asymptotic formula","score":0.7739999890327454}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9208999872207642},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6327999830245972},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.5584999918937683},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.508400022983551},{"id":"https://openalex.org/C190565394","wikidata":"https://www.wikidata.org/wiki/Q6935001","display_name":"Multiplicative number theory","level":4,"score":0.491100013256073},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.483599990606308},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4643000066280365},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4641999900341034},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4523000121116638},{"id":"https://openalex.org/C40758505","wikidata":"https://www.wikidata.org/wiki/Q386292","display_name":"Prime number theorem","level":3,"score":0.44269999861717224},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.4178999960422516},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.3625999987125397},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.3547999858856201},{"id":"https://openalex.org/C130498168","wikidata":"https://www.wikidata.org/wiki/Q170008","display_name":"Arithmetic progression","level":2,"score":0.3418000042438507},{"id":"https://openalex.org/C30860621","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime factor","level":3,"score":0.34130001068115234},{"id":"https://openalex.org/C174072685","wikidata":"https://www.wikidata.org/wiki/Q1667469","display_name":"Prime power","level":3,"score":0.3188000023365021},{"id":"https://openalex.org/C24209939","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic formula","level":2,"score":0.3043999969959259},{"id":"https://openalex.org/C11067248","wikidata":"https://www.wikidata.org/wiki/Q7243373","display_name":"Prime k-tuple","level":4,"score":0.30309998989105225},{"id":"https://openalex.org/C143352335","wikidata":"https://www.wikidata.org/wiki/Q110863","display_name":"Twin prime","level":3,"score":0.2964000105857849},{"id":"https://openalex.org/C196644772","wikidata":"https://www.wikidata.org/wiki/Q3884964","display_name":"Orbit (dynamics)","level":2,"score":0.28380000591278076},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.27810001373291016},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.2754000127315521},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.26579999923706055},{"id":"https://openalex.org/C44115641","wikidata":"https://www.wikidata.org/wiki/Q918099","display_name":"Ramsey's theorem","level":3,"score":0.26499998569488525}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.28200","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.28200","pdf_url":"https://arxiv.org/pdf/2609.28200","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.2609.28200","doi":"https://doi.org/10.48550/arxiv.2609.28200","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.28200","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","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.28200","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.28200","pdf_url":"https://arxiv.org/pdf/2609.28200","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214244175.pdf","grobid_xml":"https://content.openalex.org/works/W7214244175.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1981711978","https://openalex.org/W7098726121","https://openalex.org/W2071729934","https://openalex.org/W2953014873","https://openalex.org/W4417422315","https://openalex.org/W2951827544","https://openalex.org/W2046541871","https://openalex.org/W2272485272","https://openalex.org/W2770206178","https://openalex.org/W4287686587"],"abstract_inverted_index":{"Friedlander":[0],"and":[1,64],"Iwaniec":[2],"proved":[3],"that":[4,86,103],"the":[5,10,21,25,37,43,52,78,87,104,118,133,138],"number":[6,119],"of":[7,9,24,33,54,74,109,120,128],"points":[8],"orbit":[11],"$\\{\u03b3i":[12],"\\colon":[13],"\u03b3\\in\\SL_2(\\Z)\\}$":[14],"lying":[15],"at":[16,92,141],"a":[17,48,126],"distance":[18],"$p-2$":[19],"from":[20],"origin":[22],"$i$":[23],"upper":[26,38],"half-plane,":[27],"with":[28,91,140],"$p\\le":[29],"x$":[30],"prime,":[31],"is":[32,40,73,117],"order":[34,75],"$x/\\log":[35],"x$;":[36],"bound":[39,136],"unconditional,":[41],"while":[42],"lower":[44,135],"one":[45],"rests":[46],"on":[47],"strong":[49],"hypothesis":[50],"concerning":[51],"distribution":[53,110],"primes":[55],"in":[56,112],"arithmetic":[57,113],"progressions.":[58],"We":[59],"consider":[60],"instead":[61],"square-free":[62,88],"distances":[63,89,139],"prove":[65],"unconditionally":[66,85],"an":[67],"asymptotic":[68],"formula,":[69],"whose":[70],"main":[71],"term":[72],"$x$.":[76],"Employing":[77],"weighted":[79],"linear":[80],"sieve,":[81],"we":[82,131],"also":[83],"show":[84],"$n$":[90,124],"most":[93,142],"$7$":[94,148],"prime":[95,144],"factors":[96,145],"contribute":[97],"$\\gg":[98],"x/\\log":[99],"x$.":[100],"Finally,":[101],"assuming":[102],"sequence":[105],"$r(n-2)r(n+2)$":[106],"has":[107],"level":[108],"$x^\u03b8$":[111],"progressions,":[114],"where":[115],"$r(n)$":[116],"ways":[121],"to":[122,150],"write":[123],"as":[125],"sum":[127],"two":[129],"squares,":[130],"obtain":[132],"same":[134],"for":[137],"$N$":[143],"(the":[146],"value":[147],"corresponds":[149],"$\u03b8=1/6$).":[151]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-25T00:00:00"}
