{"id":"https://openalex.org/W7204179998","doi":"https://doi.org/10.48550/arxiv.2608.23006","title":"Dyadic denominator bounds and a transfer principle for the phase constants of Jacobi zeros","display_name":"Dyadic denominator bounds and a transfer principle for the phase constants of Jacobi zeros","publication_year":2026,"publication_date":"2026-08-24","ids":{"openalex":"https://openalex.org/W7204179998","doi":"https://doi.org/10.48550/arxiv.2608.23006"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.23006","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.23006","pdf_url":"https://arxiv.org/pdf/2608.23006","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":"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/2608.23006","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024820291","display_name":"Iv\u00e1n Area","orcid":"https://orcid.org/0000-0003-0872-5017","observed_orcids":["https://orcid.org/0000-0003-0872-5017"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Area, Iv\u00e1n","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5024820291"],"corresponding_institution_ids":[],"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/T11191","display_name":"Mathematical functions and polynomials","score":0.7997999787330627,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.7997999787330627,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.08560000360012054,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.07010000199079514,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/jacobi-polynomials","display_name":"Jacobi polynomials","score":0.9810000061988831},{"id":"https://openalex.org/keywords/phase-constant","display_name":"phase constant","score":0.6359999775886536},{"id":"https://openalex.org/keywords/large-degree-asymptotics","display_name":"large degree asymptotics","score":0.6510000228881836},{"id":"https://openalex.org/keywords/2-adic-valuation","display_name":"2-adic valuation","score":0.9300000071525574},{"id":"https://openalex.org/keywords/2-adic-numbers","display_name":"2-adic numbers","score":0.777999997138977},{"id":"https://openalex.org/keywords/binomial-sums","display_name":"binomial sums","score":0.5239999890327454},{"id":"https://openalex.org/keywords/power-series","display_name":"power series","score":0.6100000143051147},{"id":"https://openalex.org/keywords/transfer-principle","display_name":"transfer principle","score":0.5460000038146973}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8424999713897705},{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.5217999815940857},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.4458000063896179},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.43560001254081726},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43209999799728394},{"id":"https://openalex.org/C48490523","wikidata":"https://www.wikidata.org/wiki/Q371631","display_name":"Jacobi polynomials","level":3,"score":0.4223000109195709},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.42080000042915344},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.39430001378059387},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.391400009393692},{"id":"https://openalex.org/C186027771","wikidata":"https://www.wikidata.org/wiki/Q4008379","display_name":"Valuation (finance)","level":2,"score":0.326200008392334},{"id":"https://openalex.org/C68827188","wikidata":"https://www.wikidata.org/wiki/Q674533","display_name":"Inverse trigonometric functions","level":2,"score":0.3239000141620636},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3116999864578247},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.31040000915527344},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.2915000021457672},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.28769999742507935},{"id":"https://openalex.org/C165656649","wikidata":"https://www.wikidata.org/wiki/Q748339","display_name":"Legendre symbol","level":5,"score":0.2632000148296356},{"id":"https://openalex.org/C185767445","wikidata":"https://www.wikidata.org/wiki/Q207952","display_name":"Law of large numbers","level":3,"score":0.2597000002861023}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.23006","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.23006","pdf_url":"https://arxiv.org/pdf/2608.23006","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.23006","doi":"https://doi.org/10.48550/arxiv.2608.23006","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.23006","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:2608.23006","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.23006","pdf_url":"https://arxiv.org/pdf/2608.23006","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":"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/W7204179998.pdf","grobid_xml":"https://content.openalex.org/works/W7204179998.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W1802466452","https://openalex.org/W2033923703","https://openalex.org/W2052078837","https://openalex.org/W2078742163","https://openalex.org/W2079025955","https://openalex.org/W2125369296","https://openalex.org/W2260956954","https://openalex.org/W3196002052","https://openalex.org/W4242849907","https://openalex.org/W4252939931","https://openalex.org/W4293200472","https://openalex.org/W4415694110"],"related_works":["https://openalex.org/W202437774","https://openalex.org/W1839098345","https://openalex.org/W7214400205","https://openalex.org/W2002665424","https://openalex.org/W1603896446","https://openalex.org/W7095660575","https://openalex.org/W4247047306","https://openalex.org/W4214871208","https://openalex.org/W1966898730","https://openalex.org/W7221164838"],"abstract_inverted_index":{"A":[0],"formal":[1],"large-degree":[2],"phase":[3],"expansion":[4],"associated":[5],"with":[6,30,80],"the":[7,10,51,59,63,72,85,91,96,108,120,131,148],"zeros":[8],"of":[9,17,21,53,62,66,74,90,124,147,151],"Jacobi":[11],"polynomial":[12,25],"$P_n^{(\u03b1,\u03b2)}$":[13],"contains":[14],"a":[15,24,39,152,165],"sequence":[16],"constants":[18],"$\u03ba_1,\u03ba_2,\\dots$,":[19],"each":[20],"which":[22,43,47,102],"is":[23,76,84,114,136,141,162,169],"in":[26,50,119,157,164],"$\u03b1^2$":[27],"and":[28,45,70,168],"$\u03b2^2$":[29],"rational":[31],"coefficients;":[32],"for":[33,138,176],"instance":[34],"$\u03ba_1=(\u03b1^2-\u03b2^2)/4$.":[35],"This":[36],"paper":[37],"asks":[38],"simple":[40],"arithmetic":[41],"question:":[42],"primes,":[44],"to":[46,95,117,143],"powers,":[48],"occur":[49],"denominators":[52],"these":[54],"coefficients?":[55],"We":[56],"prove":[57,104],"that":[58,71,107,130],"odd":[60],"part":[61],"common":[64],"denominator":[65],"$\u03ba_r$":[67],"divides":[68],"$\\operatorname{lcm}(1,3,\\ldots,2r-1)$,":[69],"power":[73,155],"$2$":[75],"at":[77],"most":[78],"$2^{E_r}$":[79],"$E_r=3r-1+\u03bd_2((r-1)!)$,":[81],"where":[82],"$\u03bd_2$":[83],"$2$-adic":[86,125],"valuation.":[87],"The":[88],"study":[89],"leading":[92],"coefficient":[93],"leads":[94],"formula":[97],"\\[":[98],"\u03bd_2\\!\\left(\\sum_{j=0}^{m}\\binom":[99],"mj\\frac1{2j+1}\\right)=m+\u03bd_2(m+1)\\qquad(m\\ge0),":[100],"\\]":[101],"we":[103,128],"by":[105,173],"showing":[106],"series":[109,156],"$\\sum_{k\\ge0}k!/(2k+1)!!$,":[110],"whose":[111],"real":[112],"sum":[113],"$\u03c0/2$,":[115],"converges":[116],"$0$":[118],"field":[121],"$\\mathbb":[122],"Q_2$":[123],"numbers.":[126],"Finally,":[127],"show":[129],"statement":[132],"``the":[133],"exponent":[134],"$E_r$":[135],"attained":[137],"every":[139],"$r$''":[140],"equivalent":[142],"an":[144],"integrality":[145],"property":[146,161],"Taylor":[149],"coefficients":[150],"single":[153],"explicit":[154],"one":[158],"variable.":[159],"That":[160],"established":[163],"separate":[166],"paper,":[167],"confirmed":[170],"here":[171],"independently,":[172],"exact":[174],"computation,":[175],"$r\\le48$.":[177]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-08-26T00:00:00"}
