{"id":"https://openalex.org/W7225617013","doi":"https://doi.org/10.5281/zenodo.24094317","title":"Three-point correlation of the Riemann zeros at finite height: the ratios conjecture bin by bin on 147 million zeros up to t = 3e10, the amplitude of the deviation from GUE, and smaller sets further up - a reproducible numerical study IV","display_name":"Three-point correlation of the Riemann zeros at finite height: the ratios conjecture bin by bin on 147 million zeros up to t = 3e10, the amplitude of the deviation from GUE, and smaller sets further up - a reproducible numerical study IV","publication_year":2026,"publication_date":"2026-11-09","ids":{"openalex":"https://openalex.org/W7225617013","doi":"https://doi.org/10.5281/zenodo.24094317"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24094317","doi":"https://doi.org/10.5281/zenodo.24094317","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24094317","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.24094317","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135678626","display_name":"David Hess","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hess, David","raw_affiliation_strings":["MAYAN ALFA V1008 LAB v.34.72"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MAYAN ALFA V1008 LAB v.34.72","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5135678626"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9994999766349792,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/zeros-of-the-riemann-zeta-function","display_name":"Riemann zeta function zeros","score":0.8859999775886536},{"id":"https://openalex.org/keywords/three-point-correlations","display_name":"three-point correlations","score":0.7940000295639038},{"id":"https://openalex.org/keywords/gaussian-unitary-ensemble","display_name":"Gaussian unitary ensemble","score":0.48399999737739563},{"id":"https://openalex.org/keywords/random-matrix-theory","display_name":"random matrix theory","score":0.546999990940094},{"id":"https://openalex.org/keywords/riemann-zeta-function","display_name":"Riemann zeta function","score":0.7839999794960022},{"id":"https://openalex.org/keywords/low-lying-zeros","display_name":"low-lying zeros","score":0.6190000176429749},{"id":"https://openalex.org/keywords/numerical-verification","display_name":"numerical verification","score":0.3240000009536743},{"id":"https://openalex.org/keywords/chi-square-test","display_name":"chi-square test","score":0.4749999940395355},{"id":"https://openalex.org/keywords/unitary-matrices","display_name":"unitary matrices","score":0.5270000100135803}],"concepts":[{"id":"https://openalex.org/C156273044","wikidata":"https://www.wikidata.org/wiki/Q4913766","display_name":"Bin","level":2,"score":0.9254999756813049},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8116999864578247},{"id":"https://openalex.org/C22679943","wikidata":"https://www.wikidata.org/wiki/Q159375","display_name":"Standard deviation","level":2,"score":0.4657000005245209},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.46459999680519104},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.454800009727478},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4546000063419342},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43140000104904175},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4108000099658966},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4083999991416931},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3736000061035156},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.35499998927116394},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.3515999913215637},{"id":"https://openalex.org/C53622274","wikidata":"https://www.wikidata.org/wiki/Q2496679","display_name":"Correlation function (quantum field theory)","level":3,"score":0.32899999618530273},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.32100000977516174},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.3061000108718872},{"id":"https://openalex.org/C117220453","wikidata":"https://www.wikidata.org/wiki/Q5172842","display_name":"Correlation","level":2,"score":0.2964000105857849},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.29350000619888306},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.29339998960494995},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28839999437332153},{"id":"https://openalex.org/C2988709989","wikidata":"https://www.wikidata.org/wiki/Q85784623","display_name":"Mean square","level":2,"score":0.2786000072956085},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.2687000036239624},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.266400009393692},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.2651999890804291}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24094317","doi":"https://doi.org/10.5281/zenodo.24094317","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24094317","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},{"id":"doi:10.5281/zenodo.24094318","doi":"https://doi.org/10.5281/zenodo.24094318","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24094318","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":"doi:10.5281/zenodo.24094317","doi":"https://doi.org/10.5281/zenodo.24094317","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24094317","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7101031783","https://openalex.org/W2105566496","https://openalex.org/W7212389603","https://openalex.org/W7142332167","https://openalex.org/W7119491322","https://openalex.org/W7220964926","https://openalex.org/W7095991159","https://openalex.org/W2005948101","https://openalex.org/W2006769311","https://openalex.org/W7142231191"],"abstract_inverted_index":{"Fourth":[0],"study":[1,8,11,331,351,566],"of":[2,20,23,82,90,96,99,131,135,149,204,230,259,272,283,325,339,355,401,420,454,483,511,557,565,573],"the":[3,16,21,24,38,47,57,73,80,118,129,132,136,147,152,160,168,187,215,231,246,267,270,277,281,310,359,372,377,391,402,404,413,421,429,435,438,442,471,484,498,517,532,538,543,555,558,563,571],"series":[4],"(study":[5],"I:":[6],"doi:10.5281/zenodo.23815328;":[7],"II:":[9],"doi:10.5281/zenodo.23928017;":[10],"III:":[12],"doi:10.5281/zenodo.23991165).":[13],"It":[14],"measures":[15],"three-point":[17],"correlation":[18],"R3":[19,213],"zeros":[22,63,98,121,316,539,556],"Riemann":[25,518],"zeta":[26],"function":[27],"at":[28,209,342,457,462],"finite":[29],"height":[30],"and":[31,42,93,107,114,201,226,312,366,394,437,489,523,531,545,548,554,568,578],"compares":[32],"it":[33],"bin":[34,36,84,151,157,171,173,176,216,364],"by":[35,65,172,480,550,562],"with":[37,146,257,264,308,352,497],"formula":[39,153,169,188,278,311],"that":[40,112,493,534],"Conrey":[41,113],"Snaith":[43,115],"(2008)":[44],"derived":[45],"from":[46,72,86,197,248,390,542],"ratios":[48,360,392,414,439],"conjecture,":[49,507],"which":[50],"contains":[51],"all":[52,165,255],"lower-order":[53],"terms":[54],"down":[55],"to":[56,76,330],"constant":[58],"term.":[59],"Data:":[60],"147.2":[61],"million":[62],"computed":[64,348],"D.":[66],"Platt":[67],"(LMFDB)":[68],"in":[69,214,254,336,382,521],"14":[70,166],"blocks":[71,167,256,269],"first":[74,119],"zero":[75],"t":[77,103,210],"=":[78,104,211,241,252,302,344],"3.06e10,":[79,212],"error":[81,148,324],"every":[83,150,356,536,574],"estimated":[85],"40":[87],"consecutive":[88,273,455],"pieces":[89,274],"each":[91,284],"block,":[92],"three":[94,298,337],"sets":[95,293,299],"1e4":[97],"A.":[100],"Odlyzko":[101],"near":[102,317,376,447],"2.7e11,":[105],"1.4e20":[106],"1.4e21.":[108],"(i)":[109],"The":[110,451],"differences":[111],"reported":[116],"for":[117,143,322,349,396,426,505],"1e5":[120],"(standard":[122],"deviation":[123,247],"about":[124,220,314],"0.03,":[125],"maximum":[126],"0.164)":[127],"have":[128],"size":[130,207],"counting":[133],"noise":[134],"triples":[137],"(0.027":[138],"against":[139,159,388,459,570],"0.0265":[140],"+-":[141,304,386],"0.0007":[142],"pure":[144],"noise);":[145],"agrees,":[154],"chi2":[155],"per":[156,175,363],"1.050":[158],"expected":[161],"1.054.":[162],"(ii)":[163],"In":[164],"agrees":[170],"(chi2":[174,362],"0.905-1.145,":[177],"mean":[178],"1.038,":[179],"784":[180],"bins":[181],"each),":[182],"while":[183],"GUE":[184,225,249],"gives":[185,250],"6.4-117,":[186],"without":[189],"its":[190],"arithmetic":[191],"factors":[192],"5.0-90,":[193],"a":[194,418,467,486,506,509],"model":[195],"built":[196],"pairs":[198],"alone":[199,431],"2.7-37":[200],"unitary":[202],"matrices":[203],"an":[205,323,328,490],"effective":[206],"27-446;":[208],"(0.5-0.6)^2":[217],"is":[218,502],"still":[219],"31":[221],"standard":[222,369],"errors":[223,229,258,370],"below":[224,444],"within":[227],"1.6":[228],"formula.":[232],"(iii)":[233],"Written":[234],"as":[235,276,410,412],"one":[236],"amplitude,":[237],"R_data":[238],"-":[239,244,417],"R_GUE":[240],"lambda":[242],"(R_ratios":[243],"R_GUE),":[245],"lambda3":[251,301],"0.993-1.010":[253],"0.2-0.8":[260],"%,":[261],"no":[262,495],"trend":[263],"height;":[265],"inside":[266],"lowest":[268],"amplitude":[271],"falls":[275,408],"averaged":[279],"over":[280,406],"heights":[282],"piece":[285],"predicts.":[286],"(iv)":[287],"Following":[288],"S.":[289],"J.":[290],"Miller,":[291],"smaller":[292],"much":[294],"further":[295],"up:":[296],"Odlyzko's":[297,546],"give":[300],"0.62":[303],"0.38":[305],"together,":[306],"consistent":[307],"both":[309],"GUE;":[313],"1.9e5":[315],"1e21":[318],"would":[319],"be":[320],"needed":[321],"0.2.":[326],"As":[327],"addendum":[329],"III,":[332],"quadratic":[333],"Dirichlet":[334],"L-functions":[335,347,559],"bands":[338],"width":[340],"15,000":[341],"|D|":[343,448],"1e12":[345,458],"(27,355":[346],"this":[350],"PARI/GP,":[353],"SHA-256":[354,572],"block)":[357],"follow":[358],"conjecture":[361,393,415,440],"0.87-1.21)":[365],"lie":[367],"15.4":[368],"above":[371],"Katz-Sarnak":[373],"limit":[374],"USp":[375,407],"central":[378],"point":[379],"(combined":[380],"density":[381],"[0,":[383],"1/2]:":[384],"0.5040":[385],"0.0061":[387],"0.5054":[389],"0.4105":[395],"USp).":[397],"Over":[398],"eight":[399],"decades":[400],"conductor":[403],"excess":[405,443],"only":[409,446],"1/ln(|D|/pi),":[411],"predicts":[416],"slowness":[419],"kind":[422],"M.":[423],"Watkins":[424],"found":[425],"cubic":[427],"twists;":[428],"data":[430,530,579],"do":[432],"not":[433,508],"fix":[434],"limit,":[436],"brings":[441],"0.05":[445],"~":[449],"3.6e21.":[450],"band":[452,473],"statistics":[453],"discriminants":[456],"control":[460],"stretches":[461],"1e10":[463],"remain":[464],"undecided":[465],"under":[466],"rule":[468],"fixed":[469],"before":[470],"last":[472],"was":[474],"computed.":[475],"All":[476],"numbers":[477],"are":[478,540,560],"checked":[479,549,569],"null":[481],"models":[482],"pipeline,":[485],"sensitivity":[487],"analysis":[488],"independent":[491],"recomputation":[492],"shares":[494],"code":[496,583],"main":[499],"one.":[500],"Agreement":[501],"numerical":[503],"support":[504],"proof":[510],"it;":[512],"nothing":[513],"here":[514],"bears":[515],"on":[516],"hypothesis.":[519],"Article":[520],"English":[522],"Czech":[524],"(PDF,":[525],"DOCX,":[526],"LaTeX,":[527],"Markdown),":[528],"figures,":[529],"scripts":[533],"reproduce":[535],"number;":[537],"downloaded":[541],"LMFDB":[544],"pages":[547],"their":[551],"md5":[552],"sums,":[553],"regenerated":[561],"generator":[564],"III":[567],"block.":[575],"Text,":[576],"figures":[577],"CC":[580],"BY":[581],"4.0,":[582],"MIT.":[584]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}