{"id":"https://openalex.org/W7223128786","doi":"https://doi.org/10.48550/arxiv.2610.27707","title":"P\u00f3lya's conjecture for Dirichlet eigenvalues of spherical shells and Aharonov--Bohm annuli","display_name":"P\u00f3lya's conjecture for Dirichlet eigenvalues of spherical shells and Aharonov--Bohm annuli","publication_year":2026,"publication_date":"2026-10-20","ids":{"openalex":"https://openalex.org/W7223128786","doi":"https://doi.org/10.48550/arxiv.2610.27707"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.27707","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.27707","pdf_url":"https://arxiv.org/pdf/2610.27707","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/2610.27707","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159181361","display_name":"Yutian Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4400600959","display_name":"Nanfang College Guangzhou","ror":"https://ror.org/04vrxqg89","country_code":"CN","type":"education","lineage":["https://openalex.org/I4400600959"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Li, Yutian","raw_affiliation_strings":["School of Mathematics and Statistics Nanfang College , Guangzhou 510970 , Guangdong , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics Nanfang College , Guangzhou 510970 , Guangdong , China","institution_ids":["https://openalex.org/I4400600959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5159181361"],"corresponding_institution_ids":["https://openalex.org/I4400600959"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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":0.9994999766349792,"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":0.9994999766349792,"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/T11166","display_name":"Analytic Number Theory Research","score":9.999999747378752e-05,"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/T11210","display_name":"Mathematical Analysis and Transform Methods","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"}}],"keywords":[{"id":"https://openalex.org/keywords/polya-conjecture","display_name":"P\u00f3lya conjecture","score":0.8769999742507935},{"id":"https://openalex.org/keywords/dirichlet-eigenvalues","display_name":"Dirichlet eigenvalues","score":0.9440000057220459},{"id":"https://openalex.org/keywords/spherical-shell","display_name":"spherical shell","score":0.9800000190734863},{"id":"https://openalex.org/keywords/magnetic-flux","display_name":"magnetic flux","score":0.7120000123977661},{"id":"https://openalex.org/keywords/eigenvalue-counting-function","display_name":"eigenvalue counting function","score":0.8019999861717224},{"id":"https://openalex.org/keywords/weyl-s-law","display_name":"Weyl law","score":0.9100000262260437},{"id":"https://openalex.org/keywords/dimensionality-reduction","display_name":"dimensionality reduction","score":0.40400001406669617}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8133000135421753},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6121000051498413},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6044999957084656},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.5360999703407288},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5156999826431274},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5005000233650208},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.47049999237060547},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4690999984741211},{"id":"https://openalex.org/C102231394","wikidata":"https://www.wikidata.org/wiki/Q5280763","display_name":"Dirichlet eigenvalue","level":5,"score":0.4683000147342682},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.4650999903678894},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.44830000400543213},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.44690001010894775},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4219000041484833},{"id":"https://openalex.org/C150936888","wikidata":"https://www.wikidata.org/wiki/Q4769748","display_name":"Annulus (botany)","level":2,"score":0.3831999897956848},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35740000009536743},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.33739998936653137},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.32440000772476196},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.3167000114917755},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.31360000371932983},{"id":"https://openalex.org/C140142295","wikidata":"https://www.wikidata.org/wiki/Q617417","display_name":"Isoperimetric inequality","level":2,"score":0.313400000333786},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.3075000047683716},{"id":"https://openalex.org/C95611797","wikidata":"https://www.wikidata.org/wiki/Q17502105","display_name":"Infimum and supremum","level":2,"score":0.2978000044822693},{"id":"https://openalex.org/C2780297109","wikidata":"https://www.wikidata.org/wiki/Q917390","display_name":"Essential spectrum","level":3,"score":0.29159998893737793},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.2806999981403351},{"id":"https://openalex.org/C2778872062","wikidata":"https://www.wikidata.org/wiki/Q5280765","display_name":"Dirichlet form","level":4,"score":0.2621999979019165},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.25049999356269836}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.27707","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.27707","pdf_url":"https://arxiv.org/pdf/2610.27707","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.2610.27707","doi":"https://doi.org/10.48550/arxiv.2610.27707","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.27707","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:2610.27707","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.27707","pdf_url":"https://arxiv.org/pdf/2610.27707","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":[{"id":"https://openalex.org/G3001884546","display_name":null,"funder_award_id":"2025ZDJS099","funder_id":"https://openalex.org/F4320326279","funder_display_name":"Department of Education of Guangdong Province"}],"funders":[{"id":"https://openalex.org/F4320326279","display_name":"Department of Education of Guangdong Province","ror":"https://ror.org/01s5gyw91"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223128786.pdf","grobid_xml":"https://content.openalex.org/works/W7223128786.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1505371679","https://openalex.org/W1963823462","https://openalex.org/W1976809511","https://openalex.org/W2012886538","https://openalex.org/W2064790073","https://openalex.org/W2567655268","https://openalex.org/W3159864100","https://openalex.org/W4379383615","https://openalex.org/W4399130091","https://openalex.org/W4404694080","https://openalex.org/W4416046383","https://openalex.org/W4416595420","https://openalex.org/W4417423266","https://openalex.org/W7106609123","https://openalex.org/W7171650807","https://openalex.org/W7172291480","https://openalex.org/W7220698829","https://openalex.org/W7221569617","https://openalex.org/W7222048879","https://openalex.org/W7222160575"],"related_works":["https://openalex.org/W4416046383","https://openalex.org/W4399130091","https://openalex.org/W7223411965","https://openalex.org/W7220698829","https://openalex.org/W4298442822","https://openalex.org/W4379383615","https://openalex.org/W2547324628","https://openalex.org/W7223576069","https://openalex.org/W7214088354","https://openalex.org/W7222160575"],"abstract_inverted_index":{"We":[0,45],"establish":[1],"strict":[2,50,153],"Dirichlet":[3],"P\u00f3lya":[4],"inequalities":[5],"for":[6,14,52,96,114,139],"spherical":[7],"shells":[8,158],"in":[9,101,109],"every":[10,15,31],"dimension":[11,63],"$d\\ge2$":[12],"and":[13,82,108,159],"radius":[16],"ratio.":[17],"The":[18,89,128],"inclusive":[19],"eigenvalue":[20,36],"counting":[21],"function":[22],"lies":[23],"strictly":[24,37],"below":[25],"the":[26,48,53,65,74,97,102,110,115,119,125,132,135,145],"leading":[27],"Weyl":[28,40],"term":[29],"at":[30,59],"positive":[32],"energy;":[33],"consequently,":[34],"each":[35],"exceeds":[38],"its":[39],"prediction,":[41],"with":[42],"multiplicities":[43],"included.":[44],"also":[46],"prove":[47],"same":[49],"inequality":[51],"Aharonov--Bohm":[54],"operator":[55],"on":[56,155],"planar":[57,75],"annuli":[58],"arbitrary":[60],"flux.":[61,147],"In":[62],"two,":[64],"nonmagnetic":[66],"result":[67],"gives":[68],"a":[69,93,106],"fully":[70],"analytic":[71],"proof":[72],"of":[73,78,105,121,134,157],"annulus":[76],"theorem":[77],"Filonov,":[79],"Levitin,":[80],"Polterovich":[81],"Sher":[83],"(J.":[84],"Lond.":[85],"Math.":[86],"Soc.,":[87],"2026).":[88],"common":[90],"ingredient":[91],"is":[92],"lattice-point":[94],"bound":[95],"shell":[98],"action,":[99],"uniform":[100],"starting":[103],"point":[104],"tail":[107,129],"lattice":[111,142],"translation.":[112],"Quadrature":[113],"inverse":[116],"action":[117],"controls":[118],"change":[120],"convexity":[122],"caused":[123],"by":[124],"inner":[126],"boundary.":[127],"estimate":[130],"supplies":[131],"hypothesis":[133],"known":[136],"dimension-reduction":[137],"argument":[138,150],"balls,":[140],"while":[141],"translations":[143],"represent":[144],"magnetic":[146],"Laptev's":[148],"product":[149],"yields":[151],"corresponding":[152],"bounds":[154],"products":[156],"nonempty":[160],"bounded":[161],"open":[162],"sets.":[163]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-22T00:00:00"}
