{"id":"https://openalex.org/W7222221060","doi":"https://doi.org/10.48550/arxiv.2610.18943","title":"Some Bounds on the Lehmer Index","display_name":"Some Bounds on the Lehmer Index","publication_year":2026,"publication_date":"2026-10-13","ids":{"openalex":"https://openalex.org/W7222221060","doi":"https://doi.org/10.48550/arxiv.2610.18943"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.18943","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.18943","pdf_url":"https://arxiv.org/pdf/2610.18943","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/2610.18943","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5154967257","display_name":"Xiaodong Zhuang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I108688024","display_name":"Qingdao University","ror":"https://ror.org/021cj6z65","country_code":"CN","type":"education","lineage":["https://openalex.org/I108688024"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhuang, Xiaodong","raw_affiliation_strings":["Qingdao University , Shandong Province , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Qingdao University , Shandong Province , China","institution_ids":["https://openalex.org/I108688024"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5154967257"],"corresponding_institution_ids":["https://openalex.org/I108688024"],"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":0.8705999851226807,"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":0.8705999851226807,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.03150000050663948,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.023499999195337296,"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/lehmer-numbers","display_name":"Lehmer numbers","score":0.9959999918937683},{"id":"https://openalex.org/keywords/upper-bounds","display_name":"upper bounds","score":0.722000002861023},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.8730000257492065}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7705000042915344},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.6144999861717224},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.5877000093460083},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5361999869346619},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47909998893737793},{"id":"https://openalex.org/C2777382242","wikidata":"https://www.wikidata.org/wiki/Q6017816","display_name":"Index (typography)","level":2,"score":0.4560000002384186},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.367900013923645},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.367000013589859},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.29269999265670776},{"id":"https://openalex.org/C23230895","wikidata":"https://www.wikidata.org/wiki/Q104752","display_name":"Coprime integers","level":2,"score":0.2678000032901764},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2637999951839447},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.26159998774528503}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.18943","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.18943","pdf_url":"https://arxiv.org/pdf/2610.18943","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.2610.18943","doi":"https://doi.org/10.48550/arxiv.2610.18943","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.18943","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:2610.18943","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.18943","pdf_url":"https://arxiv.org/pdf/2610.18943","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/W7222221060.pdf","grobid_xml":"https://content.openalex.org/works/W7222221060.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W837905424","https://openalex.org/W2949509227","https://openalex.org/W2950185423","https://openalex.org/W4250197756","https://openalex.org/W1586565175","https://openalex.org/W2809814795","https://openalex.org/W7096878828","https://openalex.org/W4241608974","https://openalex.org/W921722221","https://openalex.org/W1970299963"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"the":[3,8,12,16,33],"relationship":[4],"is":[5,41],"studied":[6],"between":[7],"Lehmer":[9,21,34,39,46],"index":[10,40],"and":[11,26],"reciprocal":[13],"sum":[14],"of":[15,19],"prime":[17,52],"factors":[18],"a":[20,27,45],"number.":[22],"Some":[23],"upper":[24],"bounds":[25],"lower":[28],"bound":[29],"are":[30],"proposed":[31,43],"for":[32],"index.":[35],"Another":[36],"constraint":[37],"on":[38],"also":[42],"if":[44],"number":[47],"has":[48],"3":[49],"as":[50],"its":[51],"factor.":[53]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-10-16T00:00:00"}