{"id":"https://openalex.org/W1987886377","doi":"https://doi.org/10.1155/2011/534391","title":"On a Result of Levin and Ste\u010dkin","display_name":"On a Result of Levin and Ste\u010dkin","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W1987886377","doi":"https://doi.org/10.1155/2011/534391","mag":"1987886377"},"language":"en","primary_location":{"id":"doi:10.1155/2011/534391","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/534391","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2011/534391.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ijmms/2011/534391.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100362412","display_name":"Peng Gao","orcid":"https://orcid.org/0000-0002-9954-1856"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]},{"id":"https://openalex.org/I4210163295","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81","country_code":"US","type":"government","lineage":["https://openalex.org/I1311060795","https://openalex.org/I4210112577","https://openalex.org/I4210163295"]}],"countries":["SG","US"],"is_corresponding":true,"raw_author_name":"Peng Gao","raw_affiliation_strings":["Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University","Nanyang Technological University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University","institution_ids":["https://openalex.org/I172675005","https://openalex.org/I4210163295"]},{"raw_affiliation_string":"Nanyang Technological University","institution_ids":["https://openalex.org/I172675005"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100362412"],"corresponding_institution_ids":["https://openalex.org/I172675005","https://openalex.org/I4210163295"],"apc_list":{"value":1050,"currency":"USD","value_usd":1050},"apc_paid":{"value":1050,"currency":"USD","value_usd":1050},"fwci":0.5057,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.57571059,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"2011","issue":"1","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":0.9998000264167786,"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":0.9998000264167786,"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":0.9970999956130981,"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/T10849","display_name":"Finite Group Theory Research","score":0.9922000169754028,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3674048185348511},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18373391032218933}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3674048185348511},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18373391032218933}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1155/2011/534391","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/534391","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2011/534391.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:eprints.vu.edu.au:17680","is_oa":true,"landing_page_url":"https://vuir.vu.edu.au/17680/","pdf_url":"https://vuir.vu.edu.au/17680/","source":{"id":"https://openalex.org/S4306400215","display_name":"Victoria University Research Repository (Victoria University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I41156924","host_organization_name":"Victoria University of Wellington","host_organization_lineage":["https://openalex.org/I41156924"],"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":"Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.247.2157","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.247.2157","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0902.4070v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.768.8323","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.768.8323","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0902.4070.pdf","raw_type":"text"},{"id":"pmh:oai:doaj.org/article:890114cc447d4fe18e03b3e301dd13a4","is_oa":true,"landing_page_url":"https://doaj.org/article/890114cc447d4fe18e03b3e301dd13a4","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"International Journal of Mathematics and Mathematical Sciences, Vol 2011 (2011)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2011/534391","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/534391","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2011/534391.pdf","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320766","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1987886377.pdf","grobid_xml":"https://content.openalex.org/works/W1987886377.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1987321542","https://openalex.org/W2001196969","https://openalex.org/W2037750755","https://openalex.org/W2048053616","https://openalex.org/W2056125351","https://openalex.org/W2065671188","https://openalex.org/W2069605999","https://openalex.org/W2092193703","https://openalex.org/W2962851785","https://openalex.org/W6834220061"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2544423928","https://openalex.org/W2052122378","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2989452537","https://openalex.org/W4313731559"],"abstract_inverted_index":{"The":[0],"following":[1],"inequality":[2,30],"for":[3,45],"0":[4,13,46,63],"&lt;":[5,7,47,64],"p":[6,36,39,42,44,48,65],"1":[8],"and":[9,21,25,60],"a":[10,16],"n":[11],"\u2265":[12],"originates":[14],"from":[15],"study":[17],"of":[18,58],"Hardy,":[19],"Littlewood,":[20],"P\u00f3lya:":[22],".":[23],"Levin":[24,59],"Ste\u010dkin":[26,61],"proved":[27],"the":[28,32,56],"previous":[29],"with":[31],"best":[33],"constant":[34],"c":[35],"=":[37],"(":[38],"/(1":[40],"\u2212":[41],"))":[43],"\u2264":[49,66],"1/3.":[50],"In":[51],"this":[52],"paper,":[53],"we":[54],"extend":[55],"result":[57],"to":[62],"0.346.":[67]},"counts_by_year":[{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
