{"id":"https://openalex.org/W7221569617","doi":"https://doi.org/10.48550/arxiv.2610.13139","title":"Strict Dirichlet P\u00f3lya Inequality for Simply Connected Planar Domains","display_name":"Strict Dirichlet P\u00f3lya Inequality for Simply Connected Planar Domains","publication_year":2026,"publication_date":"2026-10-09","ids":{"openalex":"https://openalex.org/W7221569617","doi":"https://doi.org/10.48550/arxiv.2610.13139"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.13139","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.13139","pdf_url":"https://arxiv.org/pdf/2610.13139","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/2610.13139","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5119811630","display_name":"Quanyu Tang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tang, Quanyu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5001337574","display_name":"Zuoqin Wang","orcid":"https://orcid.org/0000-0002-8932-0590","observed_orcids":["https://orcid.org/0000-0002-8932-0590"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Zuoqin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9965999722480774,"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"}},"topics":[{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9965999722480774,"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"}},{"id":"https://openalex.org/T11210","display_name":"Mathematical Analysis and Transform Methods","score":0.00039999998989515007,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.00039999998989515007,"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/simply-connected-planar-domains","display_name":"simply connected planar domains","score":0.7940000295639038},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.8920000195503235},{"id":"https://openalex.org/keywords/dirichlet-to-neumann-map","display_name":"Dirichlet-to-Neumann map","score":0.9229999780654907},{"id":"https://openalex.org/keywords/ky-fan-inequality","display_name":"Ky Fan inequality","score":0.800000011920929},{"id":"https://openalex.org/keywords/spectral-theory","display_name":"spectral theory","score":0.328000009059906}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.810699999332428},{"id":"https://openalex.org/C167204820","wikidata":"https://www.wikidata.org/wiki/Q912058","display_name":"Simply connected space","level":2,"score":0.8102999925613403},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.7620000243186951},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6290000081062317},{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.5564000010490417},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5365999937057495},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4884999990463257},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.48669999837875366},{"id":"https://openalex.org/C98214594","wikidata":"https://www.wikidata.org/wiki/Q850275","display_name":"Conformal map","level":2,"score":0.48249998688697815},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.47429999709129333},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4287000000476837},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.41839998960494995},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3546000123023987},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.3506999909877777},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.34940001368522644},{"id":"https://openalex.org/C7402137","wikidata":"https://www.wikidata.org/wiki/Q778099","display_name":"Dirichlet integral","level":5,"score":0.3237000107765198},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.31779998540878296},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.290800005197525},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.2904999852180481},{"id":"https://openalex.org/C193435613","wikidata":"https://www.wikidata.org/wiki/Q2997928","display_name":"Connected component","level":2,"score":0.29030001163482666},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.2847999930381775},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28060001134872437},{"id":"https://openalex.org/C207803063","wikidata":"https://www.wikidata.org/wiki/Q620595","display_name":"Dirichlet series","level":4,"score":0.2732999920845032},{"id":"https://openalex.org/C99072794","wikidata":"https://www.wikidata.org/wiki/Q1500617","display_name":"Unitary group","level":3,"score":0.2685999870300293},{"id":"https://openalex.org/C53688716","wikidata":"https://www.wikidata.org/wiki/Q5659270","display_name":"Harmonic measure","level":3,"score":0.2637999951839447},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.2563999891281128},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.25519999861717224}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.13139","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.13139","pdf_url":"https://arxiv.org/pdf/2610.13139","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.2610.13139","doi":"https://doi.org/10.48550/arxiv.2610.13139","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.13139","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:2610.13139","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.13139","pdf_url":"https://arxiv.org/pdf/2610.13139","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/W7221569617.pdf","grobid_xml":"https://content.openalex.org/works/W7221569617.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1963823462","https://openalex.org/W1975172027","https://openalex.org/W1976809511","https://openalex.org/W1984514714","https://openalex.org/W1989988781","https://openalex.org/W2000437686","https://openalex.org/W2012886538","https://openalex.org/W2029966448","https://openalex.org/W2063606097","https://openalex.org/W2064790073","https://openalex.org/W2103716861","https://openalex.org/W2319585909","https://openalex.org/W2319883937","https://openalex.org/W2593605192","https://openalex.org/W3119254615","https://openalex.org/W4379383615","https://openalex.org/W4389307181","https://openalex.org/W4391988058","https://openalex.org/W4403304522","https://openalex.org/W4415520849","https://openalex.org/W4416046383","https://openalex.org/W4416595420","https://openalex.org/W4417423266","https://openalex.org/W7171650807","https://openalex.org/W7172291480","https://openalex.org/W7172451143"],"related_works":["https://openalex.org/W7223576069","https://openalex.org/W2025373466","https://openalex.org/W7218652335","https://openalex.org/W4416046383","https://openalex.org/W7218932471","https://openalex.org/W7220744580","https://openalex.org/W7223575382","https://openalex.org/W2015588114","https://openalex.org/W7223128786","https://openalex.org/W4379383615"],"abstract_inverted_index":{"We":[0],"establish":[1],"the":[2,23,35,43,58],"strict":[3],"Dirichlet":[4,28],"P\u00f3lya":[5],"inequality":[6],"on":[7],"every":[8],"bounded":[9],"simply":[10],"connected":[11],"planar":[12],"domain.":[13],"The":[14,61],"proof":[15],"uses":[16],"a":[17,48,53],"unitary":[18,31],"boundary":[19],"transport":[20],"formulation":[21],"of":[22],"Helmholtz":[24],"equation":[25],"and":[26],"relates":[27],"resonances":[29],"to":[30],"eigenphase":[32],"crossings":[33],"through":[34],"Dirichlet-to-Neumann":[36],"map.":[37],"An":[38],"exact":[39],"area":[40],"identity":[41],"yields":[42],"sharp":[44],"Weyl":[45],"coefficient,":[46],"while":[47],"Ky":[49],"Fan":[50],"estimate":[51],"leaves":[52],"strictly":[54],"positive":[55],"remainder":[56],"in":[57],"counting":[59],"estimate.":[60],"general":[62],"case":[63],"follows":[64],"by":[65],"conformal":[66],"exhaustion.":[67]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-13T00:00:00"}