{"id":"https://openalex.org/W7212002736","doi":"https://doi.org/10.48550/arxiv.2609.05835","title":"Sharp Deficiency Bounds for Meromorphic Functions in the Unit Disc","display_name":"Sharp Deficiency Bounds for Meromorphic Functions in the Unit Disc","publication_year":2026,"publication_date":"2026-09-05","ids":{"openalex":"https://openalex.org/W7212002736","doi":"https://doi.org/10.48550/arxiv.2609.05835"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.05835","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.05835","pdf_url":"https://arxiv.org/pdf/2609.05835","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/2609.05835","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113422476","display_name":"Sina Nadi","orcid":"https://orcid.org/0009-0000-9791-050X","observed_orcids":["https://orcid.org/0009-0000-9791-050X"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Nadi, Sina","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5113422476"],"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/T12812","display_name":"Meromorphic and Entire Functions","score":0.9994999766349792,"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":0.9994999766349792,"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/T10884","display_name":"Holomorphic and Operator Theory","score":9.999999747378752e-05,"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/meromorphic-functions","display_name":"meromorphic functions","score":0.8569999933242798},{"id":"https://openalex.org/keywords/unit-disk","display_name":"unit disk","score":0.9760000109672546},{"id":"https://openalex.org/keywords/nevanlinna-theory","display_name":"Nevanlinna theory","score":0.6079999804496765},{"id":"https://openalex.org/keywords/finite-order","display_name":"finite order","score":0.41200000047683716},{"id":"https://openalex.org/keywords/zeros-of-derivatives","display_name":"zeros of derivatives","score":0.5049999952316284},{"id":"https://openalex.org/keywords/sharp-constants","display_name":"sharp constants","score":0.47699999809265137},{"id":"https://openalex.org/keywords/differential-operators","display_name":"differential operators","score":0.38199999928474426},{"id":"https://openalex.org/keywords/several-complex-variables","display_name":"several complex variables","score":0.5920000076293945}],"concepts":[{"id":"https://openalex.org/C190333341","wikidata":"https://www.wikidata.org/wiki/Q217616","display_name":"Meromorphic function","level":2,"score":0.8550000190734863},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8511999845504761},{"id":"https://openalex.org/C163635466","wikidata":"https://www.wikidata.org/wiki/Q3099696","display_name":"Monic polynomial","level":3,"score":0.635200023651123},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5037999749183655},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.5030999779701233},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.490200012922287},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.47589999437332153},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.45669999718666077},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4553999900817871},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43689998984336853},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.4300999939441681},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42340001463890076},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4043999910354614},{"id":"https://openalex.org/C84316537","wikidata":"https://www.wikidata.org/wiki/Q36255","display_name":"Unit vector","level":2,"score":0.39989998936653137},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.36629998683929443},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.35420000553131104},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.35249999165534973},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.3386000096797943},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.303600013256073},{"id":"https://openalex.org/C13336665","wikidata":"https://www.wikidata.org/wiki/Q125977","display_name":"Vector space","level":2,"score":0.275299996137619},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.2711000144481659},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.26010000705718994},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.2515999972820282}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.05835","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.05835","pdf_url":"https://arxiv.org/pdf/2609.05835","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.2609.05835","doi":"https://doi.org/10.48550/arxiv.2609.05835","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.05835","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:2609.05835","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.05835","pdf_url":"https://arxiv.org/pdf/2609.05835","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/W7212002736.pdf","grobid_xml":"https://content.openalex.org/works/W7212002736.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4323042556","https://openalex.org/W1992390311","https://openalex.org/W2223044489","https://openalex.org/W2087276545","https://openalex.org/W2789697646","https://openalex.org/W7016334070","https://openalex.org/W3157587542","https://openalex.org/W2076289921","https://openalex.org/W2986298650","https://openalex.org/W2962774291"],"abstract_inverted_index":{"In":[0,69],"1986,":[1],"Shea":[2,53],"and":[3,26,54,82,103,111,116],"Sons":[4,55],"obtained":[5,45],"the":[6,19,23,40,58,84,112,125,146],"following":[7],"bound":[8],"for":[9,27,108,165],"a":[10],"meromorphic":[11],"function":[12],"$f$":[13],"of":[14,101,135,151],"finite":[15,132],"order":[16,152],"$\u03c1$":[17,115],"in":[18,99,118],"unit":[20],"disc,":[21],"under":[22,83],"hypothesis":[24],"$0<\u03bb(f)\\leq+\\infty$,":[25,72],"every":[28,109,166],"positive":[29],"integer":[30],"$n$:":[31],"\\[":[32,46,75,89],"\\sum_{a\\ne\\infty}\u03b4(a,f)":[33,47,76,90],"\\leq":[34,48,77,91],"\u03b4(0,f^{(n)})\\bigl(1+n":[35,78],"k(f)\\bigr)":[36,50,79,93],"+\\frac{2n(\u03c1+1)}{\u03bb(f)}.":[37],"\\]":[38,52,81,95],"Under":[39],"condition":[41,85],"$0<\u03b1(f)\\leq+\\infty$,":[42],"they":[43],"also":[44,122],"\u0394(0,f^{(n)})\\bigl(1+n":[49,92],"+\\frac{2n}{\u03b1(f)}.":[51],"asked":[56],"whether":[57],"factor":[59],"$2$":[60],"could":[61],"be":[62],"eliminated.":[63],"We":[64,158],"prove":[65,159],"that":[66,160],"it":[67],"can.":[68],"fact,":[70],"whenever":[71],"one":[73,87],"has":[74,88],"+\\frac{n(\u03c1+1)}{\u03bb(f)},":[80],"$0<\u03b1(f)\\leq+\\infty$":[86],"+\\frac{n}{\u03b1(f)}.":[94],"The":[96],"coefficient":[97],"$n$":[98,153],"each":[100],"$n(\u03c1+1)/\u03bb(f)$":[102],"$n/\u03b1(f)$":[104],"is":[105,121,156],"best":[106],"possible":[107],"$n$,":[110],"dependence":[113],"on":[114],"$\u03b1(f)$":[117],"these":[119],"terms":[120],"essential.":[123],"At":[124],"end,":[126],"we":[127],"extend":[128],"both":[129,161],"estimates":[130],"to":[131],"subsets":[133],"$A$":[134],"an":[136],"$n$-dimensional":[137],"complex":[138],"vector":[139],"space":[140],"$V\\subset\\mathbb{C}(z)$,":[141],"with":[142],"$f^{(n)}$":[143],"replaced":[144],"by":[145],"monic":[147],"differential":[148],"operator":[149],"$D_Vf$":[150],"whose":[154],"kernel":[155],"$V$.":[157,167],"extensions":[162],"are":[163],"sharp":[164]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-10T00:00:00"}
