{"id":"https://openalex.org/W2083538045","doi":"https://doi.org/10.1155/2011/537478","title":"Value Distribution for a Class of Small Functions in the Unit Disk","display_name":"Value Distribution for a Class of Small Functions in the Unit Disk","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2083538045","doi":"https://doi.org/10.1155/2011/537478","mag":"2083538045"},"language":"en","primary_location":{"id":"doi:10.1155/2011/537478","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/537478","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2011/537478.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/2011/537478.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030034325","display_name":"Paul A. Gunsul","orcid":null},"institutions":[{"id":"https://openalex.org/I102502594","display_name":"Northern Illinois University","ror":"https://ror.org/012wxa772","country_code":"US","type":"education","lineage":["https://openalex.org/I102502594"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Paul A. Gunsul","raw_affiliation_strings":["Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA niu.edu","Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA niu.edu","institution_ids":["https://openalex.org/I102502594"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115","institution_ids":["https://openalex.org/I102502594"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5030034325"],"corresponding_institution_ids":["https://openalex.org/I102502594"],"apc_list":{"value":1050,"currency":"USD","value_usd":1050},"apc_paid":{"value":1050,"currency":"USD","value_usd":1050},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16351188,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"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/T12812","display_name":"Meromorphic and Entire Functions","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12812","display_name":"Meromorphic and Entire Functions","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10935","display_name":"Endometriosis Research and Treatment","score":0.9455000162124634,"subfield":{"id":"https://openalex.org/subfields/2743","display_name":"Reproductive Medicine"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/meromorphic-function","display_name":"Meromorphic function","score":0.9683083891868591},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8997900485992432},{"id":"https://openalex.org/keywords/entire-function","display_name":"Entire function","score":0.6915707588195801},{"id":"https://openalex.org/keywords/unit-disk","display_name":"Unit disk","score":0.6687596440315247},{"id":"https://openalex.org/keywords/nevanlinna-theory","display_name":"Nevanlinna theory","score":0.6393961906433105},{"id":"https://openalex.org/keywords/complex-plane","display_name":"Complex plane","score":0.638953685760498},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5943091511726379},{"id":"https://openalex.org/keywords/transcendental-function","display_name":"Transcendental function","score":0.5870209336280823},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5226925611495972},{"id":"https://openalex.org/keywords/unit","display_name":"Unit (ring theory)","score":0.5103616118431091},{"id":"https://openalex.org/keywords/l-function","display_name":"L-function","score":0.497452050447464},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.49556124210357666},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.46152013540267944},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.43066102266311646},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.42927539348602295},{"id":"https://openalex.org/keywords/analytic-function","display_name":"Analytic function","score":0.42669785022735596},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.41686737537384033},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38259774446487427}],"concepts":[{"id":"https://openalex.org/C190333341","wikidata":"https://www.wikidata.org/wiki/Q217616","display_name":"Meromorphic function","level":2,"score":0.9683083891868591},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8997900485992432},{"id":"https://openalex.org/C6128204","wikidata":"https://www.wikidata.org/wiki/Q847600","display_name":"Entire function","level":2,"score":0.6915707588195801},{"id":"https://openalex.org/C47177299","wikidata":"https://www.wikidata.org/wiki/Q2390323","display_name":"Unit disk","level":2,"score":0.6687596440315247},{"id":"https://openalex.org/C2780704165","wikidata":"https://www.wikidata.org/wiki/Q1281926","display_name":"Nevanlinna theory","level":3,"score":0.6393961906433105},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.638953685760498},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5943091511726379},{"id":"https://openalex.org/C43321923","wikidata":"https://www.wikidata.org/wiki/Q864333","display_name":"Transcendental function","level":2,"score":0.5870209336280823},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5226925611495972},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.5103616118431091},{"id":"https://openalex.org/C55229022","wikidata":"https://www.wikidata.org/wiki/Q1789063","display_name":"L-function","level":3,"score":0.497452050447464},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.49556124210357666},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.46152013540267944},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.43066102266311646},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.42927539348602295},{"id":"https://openalex.org/C205979905","wikidata":"https://www.wikidata.org/wiki/Q215084","display_name":"Analytic function","level":2,"score":0.42669785022735596},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.41686737537384033},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38259774446487427},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2011/537478","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/537478","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2011/537478.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:RePEc:hin:jijmms:537478","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/IJMMS/2011/537478.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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:doaj.org/article:11eb3a14b0f3452cbf9c40f721816f54","is_oa":false,"landing_page_url":"https://doaj.org/article/11eb3a14b0f3452cbf9c40f721816f54","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":null,"license_id":null,"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:10.1155/2011/537478","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/537478","pdf_url":"https://downloads.hindawi.com/journals/ijmms/2011/537478.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":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2083538045.pdf","grobid_xml":"https://content.openalex.org/works/W2083538045.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W146092479","https://openalex.org/W1509839166","https://openalex.org/W1967675979","https://openalex.org/W1974018266","https://openalex.org/W2066601492","https://openalex.org/W2081176651","https://openalex.org/W2094657415","https://openalex.org/W2153466827","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2885865066","https://openalex.org/W2089875019","https://openalex.org/W3183290492","https://openalex.org/W2961696729","https://openalex.org/W2381741678","https://openalex.org/W1980642723","https://openalex.org/W2083538045","https://openalex.org/W34983842","https://openalex.org/W2069945599","https://openalex.org/W646666776"],"abstract_inverted_index":{"If":[0,104],"f":[1,21,28,67,72,81,105,154,157,166],"is":[2,106],"a":[3,49,90,107,188],"meromorphic":[4,51,108,140],"function":[5,16,52,100,109],"in":[6,53,110,143,183,187],"the":[7,54,98,111,126,137,176,184,202],"complex":[8],"plane,":[9],"R.":[10],"Nevanlinna":[11,102],"noted":[12],"that":[13,56],"its":[14,31],"characteristic":[15],"T":[17,77,162],"(":[18,64,68,76,78,151,161,163],"r":[19,40,65,79,84,152,164,169],",":[20,62,66,80,87,147,148,153,165],")":[22,70,73,158],"could":[23],"be":[24],"used":[25],"to":[26,30,125,218],"categorize":[27],"according":[29],"rate":[32],"of":[33,92,101,139,175,211],"growth":[34],"as":[35,83,168],"|":[36,38,120],"z":[37,117,119],"=":[39,74,115,159],"\u2192":[41,85,170],"\u221e":[42,86],".":[43,131],"Later":[44],"H.":[45],"Milloux":[46],"showed":[47],"for":[48,57,145,194],"transcendental":[50],"plane":[55],"each":[58],"positive":[59],"integer":[60],"k":[61,69],"m":[63,96,150],"/":[71,156],"o":[75,160],"))":[82,167],"possibly":[88],"outside":[89],"set":[91],"finite":[93],"measure":[94],"where":[95,181],"denotes":[97],"proximity":[99],"theory.":[103],"unit":[112],"disk":[113],"D":[114,144],"{":[116],":|":[118],"<":[121],"1},":[122],"analogous":[123],"results":[124],"previous":[127],"equation":[128],"exist":[129],"when":[130],"In":[132],"this":[133],"paper,":[134],"we":[135],"consider":[136],"class":[138,177,185,203],"functions":[141,182],"\ud835\udcab":[142,204],"which":[146,195],"and":[149,178,205,209,214],"\u2032":[155],"1.":[171],"We":[172,197],"explore":[173,199],"characteristics":[174],"some":[179],"places":[180],"behave":[186],"significantly":[189],"different":[190],"manner":[191],"than":[192],"those":[193],"holds.":[196],"also":[198],"connections":[200],"between":[201],"linear":[206],"differential":[207,212],"equations":[208],"values":[210],"polynomials":[213],"give":[215],"an":[216],"analogue":[217],"Nevanlinna\u2032s":[219],"five\u2010value":[220],"theorem.":[221]},"counts_by_year":[],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}