{"id":"https://openalex.org/W7221833191","doi":"https://doi.org/10.48550/arxiv.2610.15140","title":"On a variant of the Piatetski-Shapiro prime number theorem","display_name":"On a variant of the Piatetski-Shapiro prime number theorem","publication_year":2026,"publication_date":"2026-10-10","ids":{"openalex":"https://openalex.org/W7221833191","doi":"https://doi.org/10.48550/arxiv.2610.15140"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.15140","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.15140","pdf_url":"https://arxiv.org/pdf/2610.15140","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/2610.15140","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017288006","display_name":"Linji Long","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Long, Linji","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101594881","display_name":"Jinjiang Li","orcid":"https://orcid.org/0000-0002-3204-4046","observed_orcids":["https://orcid.org/0000-0002-3204-4046"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Jinjiang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5158759364","display_name":"Min Zhang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Min","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"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":9.999999747378752e-05,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/prime-counting-function","display_name":"prime counting function","score":0.6119999885559082},{"id":"https://openalex.org/keywords/asymptotic-formula","display_name":"asymptotic formula","score":0.953000009059906},{"id":"https://openalex.org/keywords/prime-powers","display_name":"prime powers","score":0.3919999897480011},{"id":"https://openalex.org/keywords/sieve-theory","display_name":"sieve theory","score":0.36399999260902405}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8396000266075134},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.532800018787384},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4860000014305115},{"id":"https://openalex.org/C24209939","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic formula","level":2,"score":0.4690000116825104},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.43939998745918274},{"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/C11067248","wikidata":"https://www.wikidata.org/wiki/Q7243373","display_name":"Prime k-tuple","level":4,"score":0.31349998712539673},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.2702000141143799},{"id":"https://openalex.org/C174072685","wikidata":"https://www.wikidata.org/wiki/Q1667469","display_name":"Prime power","level":3,"score":0.26910001039505005},{"id":"https://openalex.org/C30860621","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime factor","level":3,"score":0.2565999925136566}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.15140","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.15140","pdf_url":"https://arxiv.org/pdf/2610.15140","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.2610.15140","doi":"https://doi.org/10.48550/arxiv.2610.15140","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.15140","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:2610.15140","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.15140","pdf_url":"https://arxiv.org/pdf/2610.15140","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":[{"id":"https://openalex.org/G2900710960","display_name":null,"funder_award_id":"12471009","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G382562614","display_name":null,"funder_award_id":"11901566","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G55069091","display_name":null,"funder_award_id":"12301006","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6461339978","display_name":null,"funder_award_id":"12001047","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221833191.pdf","grobid_xml":"https://content.openalex.org/works/W7221833191.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7137806239","https://openalex.org/W4415200222","https://openalex.org/W4415198075","https://openalex.org/W1440477637","https://openalex.org/W2766219387","https://openalex.org/W7204555174","https://openalex.org/W7171938036","https://openalex.org/W2137666454","https://openalex.org/W2010268749","https://openalex.org/W7077055573"],"abstract_inverted_index":{"Denote":[0],"by":[1],"$\u03a0_\u03b3(x)$":[2],"the":[3,24,42,51],"number":[4],"of":[5,45],"primes":[6],"$p":[7],"\\leqslant":[8],"x$":[9],"such":[10],"that":[11,23,50],"$[p^{1/\u03b3}]$":[12],"is":[13,21],"also":[14],"a":[15],"prime.":[16],"In":[17],"this":[18],"paper,":[19],"it":[20],"proved":[22],"expected":[25],"asymptotic":[26,53],"formula":[27,54],"\\begin{equation*}":[28],"\u03a0_\u03b3(x)=\\frac{\u03b3x}{(\\log":[29],"x)^2}":[30],"(1+o(1))":[31],"\\end{equation*}":[32],"holds":[33,55],"for":[34,56],"$\u03b3>":[35,57],"15/13$,":[36],"which":[37],"constitutes":[38],"an":[39],"improvement":[40],"upon":[41],"previous":[43],"result":[44],"Balog":[46],"[2]":[47],"who":[48],"showed":[49],"above":[52],"6/5$.":[58]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-15T00:00:00"}
