{"id":"https://openalex.org/W7204920265","doi":"https://doi.org/10.48550/arxiv.2608.30284","title":"A Note on the Converse Sendov Problem","display_name":"A Note on the Converse Sendov Problem","publication_year":2026,"publication_date":"2026-08-31","ids":{"openalex":"https://openalex.org/W7204920265","doi":"https://doi.org/10.48550/arxiv.2608.30284"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.30284","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30284","pdf_url":"https://arxiv.org/pdf/2608.30284","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/2608.30284","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5117439082","display_name":"Dragomir Grozev","orcid":"https://orcid.org/0009-0004-6365-2388","observed_orcids":["https://orcid.org/0009-0004-6365-2388"]},"institutions":[{"id":"https://openalex.org/I190032430","display_name":"University of Library Studies and Information Technologies","ror":"https://ror.org/001nkz398","country_code":"BG","type":"education","lineage":["https://openalex.org/I190032430"]},{"id":"https://openalex.org/I24768866","display_name":"Bulgarian Academy of Sciences","ror":"https://ror.org/01x8hew03","country_code":"BG","type":"government","lineage":["https://openalex.org/I24768866"]},{"id":"https://openalex.org/I4210105926","display_name":"Institute of Mathematics and Informatics","ror":"https://ror.org/01b5dy719","country_code":"BG","type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4210105926"]}],"countries":["BG"],"is_corresponding":false,"raw_author_name":"Grozev, Dragomir","raw_affiliation_strings":["Faculty of Information Sciences , State University of Library Studies and Informa- tion Technologies , Shipchenski prohod 69A , 1574 Sofia , Bulgaria","Institute of Mathematics and Informatics , Bulgarian Academy of Sciences , Acad. G. Bonchev 8 , 1113 Sofia , Bulgaria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Information Sciences , State University of Library Studies and Informa- tion Technologies , Shipchenski prohod 69A , 1574 Sofia , Bulgaria","institution_ids":["https://openalex.org/I190032430"]},{"raw_affiliation_string":"Institute of Mathematics and Informatics , Bulgarian Academy of Sciences , Acad. G. Bonchev 8 , 1113 Sofia , Bulgaria","institution_ids":["https://openalex.org/I24768866","https://openalex.org/I4210105926"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5132775511","display_name":"Nikolai Nikolov","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I24768866","display_name":"Bulgarian Academy of Sciences","ror":"https://ror.org/01x8hew03","country_code":"BG","type":"government","lineage":["https://openalex.org/I24768866"]},{"id":"https://openalex.org/I4210105926","display_name":"Institute of Mathematics and Informatics","ror":"https://ror.org/01b5dy719","country_code":"BG","type":"facility","lineage":["https://openalex.org/I24768866","https://openalex.org/I4210105926"]}],"countries":["BG"],"is_corresponding":false,"raw_author_name":"Nikolov, Nikolai","raw_affiliation_strings":["Institute of Mathematics and Informatics , Bulgarian Academy of Sciences , Acad. G. Bonchev 8 , 1113 Sofia , Bulgaria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Informatics , Bulgarian Academy of Sciences , Acad. G. Bonchev 8 , 1113 Sofia , Bulgaria","institution_ids":["https://openalex.org/I24768866","https://openalex.org/I4210105926"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"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/T11822","display_name":"Analytic and geometric function theory","score":0.6942999958992004,"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"}},"topics":[{"id":"https://openalex.org/T11822","display_name":"Analytic and geometric function theory","score":0.6942999958992004,"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"}},{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.19210000336170197,"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":0.03739999979734421,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polynomial-roots","display_name":"polynomial roots","score":0.6949999928474426},{"id":"https://openalex.org/keywords/critical-points","display_name":"critical points","score":0.8619999885559082},{"id":"https://openalex.org/keywords/unit-disk","display_name":"unit disk","score":0.7200000286102295},{"id":"https://openalex.org/keywords/logarithmic-derivative","display_name":"logarithmic derivative","score":0.8730000257492065},{"id":"https://openalex.org/keywords/equality-cases","display_name":"equality cases","score":0.46000000834465027}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8709999918937683},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.7839999794960022},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5550000071525574},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5515000224113464},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5336999893188477},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.4742000102996826},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.44859999418258667},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4438999891281128},{"id":"https://openalex.org/C126875415","wikidata":"https://www.wikidata.org/wiki/Q203425","display_name":"Unit circle","level":2,"score":0.4083999991416931},{"id":"https://openalex.org/C122637931","wikidata":"https://www.wikidata.org/wiki/Q118084","display_name":"Unit (ring theory)","level":2,"score":0.40059998631477356},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.3939000070095062},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3865000009536743},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.3497999906539917},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.3328999876976013},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32910001277923584},{"id":"https://openalex.org/C3098717","wikidata":"https://www.wikidata.org/wiki/Q1144872","display_name":"Modulus of continuity","level":3,"score":0.31220000982284546},{"id":"https://openalex.org/C84316537","wikidata":"https://www.wikidata.org/wiki/Q36255","display_name":"Unit vector","level":2,"score":0.30720001459121704},{"id":"https://openalex.org/C2777478746","wikidata":"https://www.wikidata.org/wiki/Q5358910","display_name":"Elementary proof","level":2,"score":0.28619998693466187},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2856000065803528},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2687000036239624},{"id":"https://openalex.org/C156387681","wikidata":"https://www.wikidata.org/wiki/Q6059484","display_name":"Invariance principle","level":2,"score":0.2526000142097473}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.30284","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30284","pdf_url":"https://arxiv.org/pdf/2608.30284","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.2608.30284","doi":"https://doi.org/10.48550/arxiv.2608.30284","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.30284","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:2608.30284","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.30284","pdf_url":"https://arxiv.org/pdf/2608.30284","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204920265.pdf","grobid_xml":"https://content.openalex.org/works/W7204920265.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2320679898","https://openalex.org/W2012090423","https://openalex.org/W1551069853","https://openalex.org/W2591762223","https://openalex.org/W2918168515","https://openalex.org/W4306801617","https://openalex.org/W2607092220","https://openalex.org/W2006381381","https://openalex.org/W3213160425","https://openalex.org/W4386617190"],"abstract_inverted_index":{"For":[0],"a":[1,21],"polynomial":[2],"of":[3,25],"degree":[4],"$n$":[5,33,42],"whose":[6],"zeros":[7],"lie":[8],"in":[9],"the":[10,16,29,36,45,67],"closed":[11],"unit":[12],"disk,":[13],"we":[14],"determine":[15],"largest":[17],"possible":[18],"distance":[19],"from":[20],"prescribed":[22],"critical":[23],"point":[24],"modulus":[26],"$r$":[27],"to":[28],"nearest":[30],"zero.":[31],"If":[32],"is":[34,39,43,48,64],"even,":[35],"sharp":[37,46],"radius":[38,47],"$\\sqrt{1-r^2}$;":[40],"if":[41],"odd,":[44],"strictly":[49],"smaller":[50],"for":[51],"$r\\in(0,1)$":[52],"and":[53,70],"depends":[54],"on":[55,66],"$n$.":[56],"Equality":[57],"cases":[58],"are":[59],"also":[60],"determined.":[61],"The":[62],"proof":[63],"based":[65],"logarithmic-derivative":[68],"identity":[69],"elementary":[71],"geometric":[72],"considerations.":[73]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-09-02T00:00:00"}
