{"id":"https://openalex.org/W2110599431","doi":"https://doi.org/10.1090/s0025-5718-2011-02573-1","title":"The zeta function on the critical line: Numerical evidence for moments and random matrix theory models","display_name":"The zeta function on the critical line: Numerical evidence for moments and random matrix theory models","publication_year":2011,"publication_date":"2011-12-19","ids":{"openalex":"https://openalex.org/W2110599431","doi":"https://doi.org/10.1090/s0025-5718-2011-02573-1","mag":"2110599431"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2011-02573-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2011-02573-1","pdf_url":"https://www.ams.org/mcom/2012-81-279/S0025-5718-2011-02573-1/S0025-5718-2011-02573-1.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2012-81-279/S0025-5718-2011-02573-1/S0025-5718-2011-02573-1.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034913308","display_name":"Ghaith A. Hiary","orcid":"https://orcid.org/0000-0002-4517-3541"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Ghaith A. Hiary","raw_affiliation_strings":["Pure Mathematics, University of Waterloo, 200 University Ave West, Waterloo, Ontario, Canada, N2L 3G1"],"affiliations":[{"raw_affiliation_string":"Pure Mathematics, University of Waterloo, 200 University Ave West, Waterloo, Ontario, Canada, N2L 3G1","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035952740","display_name":"Andrew Odlyzko","orcid":null},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Andrew M. Odlyzko","raw_affiliation_strings":["Department of Mathematics, University of Minnesota, 206 Church St. S.E., Minneapolis, Minnesota 55455"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Minnesota, 206 Church St. S.E., Minneapolis, Minnesota 55455","institution_ids":["https://openalex.org/I130238516"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034913308"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":null,"apc_paid":null,"fwci":3.6882,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.92967085,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"81","issue":"279","first_page":"1723","last_page":"1752"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9997000098228455,"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":0.9997000098228455,"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/T11716","display_name":"Random Matrices and Applications","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9995999932289124,"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/mathematics","display_name":"Mathematics","score":0.8785234689712524},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.5104707479476929},{"id":"https://openalex.org/keywords/critical-line","display_name":"Critical line","score":0.46656811237335205},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4548928141593933},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3277431130409241},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.05347329378128052}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8785234689712524},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.5104707479476929},{"id":"https://openalex.org/C2776605787","wikidata":"https://www.wikidata.org/wiki/Q5186739","display_name":"Critical line","level":2,"score":0.46656811237335205},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4548928141593933},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3277431130409241},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.05347329378128052},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-2011-02573-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2011-02573-1","pdf_url":"https://www.ams.org/mcom/2012-81-279/S0025-5718-2011-02573-1/S0025-5718-2011-02573-1.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/1290322d-d8d9-42bb-9b87-aec98f924842","is_oa":false,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/1290322d-d8d9-42bb-9b87-aec98f924842","pdf_url":null,"source":{"id":"https://openalex.org/S7407055359","display_name":"Explore Bristol Research","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Hiary, G & Odlyzko, A M 2012, 'The zetafunction on the critical line: numerical evidencefor moments and random matrix theory models', Mathematics of Computation, vol. 81, no. 279, pp. 1723-1752. https://doi.org/10.1090/S0025-5718-2011-02573-1","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2011-02573-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2011-02573-1","pdf_url":"https://www.ams.org/mcom/2012-81-279/S0025-5718-2011-02573-1/S0025-5718-2011-02573-1.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.4399999976158142}],"awards":[{"id":"https://openalex.org/G1207306512","display_name":null,"funder_award_id":"DMS-0635607","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2182150653","display_name":"FRG: L-functions and Modular Forms","funder_award_id":"0757627","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2110599431.pdf","grobid_xml":"https://content.openalex.org/works/W2110599431.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W653925602","https://openalex.org/W1498769399","https://openalex.org/W1514811612","https://openalex.org/W1538733621","https://openalex.org/W1634565696","https://openalex.org/W1636716324","https://openalex.org/W1732879935","https://openalex.org/W1973012877","https://openalex.org/W1988856634","https://openalex.org/W1990629203","https://openalex.org/W1991057622","https://openalex.org/W2013205609","https://openalex.org/W2014011150","https://openalex.org/W2015255349","https://openalex.org/W2036704739","https://openalex.org/W2040790258","https://openalex.org/W2043906885","https://openalex.org/W2049587182","https://openalex.org/W2090804474","https://openalex.org/W2093179333","https://openalex.org/W2095393613","https://openalex.org/W2101367141","https://openalex.org/W2106226212","https://openalex.org/W2148163513","https://openalex.org/W2167266655","https://openalex.org/W2334958161","https://openalex.org/W2577105026","https://openalex.org/W2808063619","https://openalex.org/W2949789930","https://openalex.org/W2962755272","https://openalex.org/W2962769128","https://openalex.org/W3103878215","https://openalex.org/W4239614637","https://openalex.org/W4243362886","https://openalex.org/W4250440028","https://openalex.org/W4251477635"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":{"Results":[0],"of":[1,4,6,52,87,105,107,110,128,140,155,162,169],"extensive":[2],"computations":[3,148],"moments":[5,45,112],"the":[7,12,50,82,85,93,103,111,126,129,138,141,156],"Riemann":[8],"zeta":[9,94,157],"function":[10,95],"on":[11,152],"critical":[13],"line":[14],"are":[15,19,64,145],"presented.":[16],"Calculated":[17],"values":[18,54,109,127,139],"compared":[20],"with":[21],"predictions":[22],"motivated":[23],"by":[24,117],"random":[25],"matrix":[26],"theory.":[27],"The":[28,147,159],"results":[29],"can":[30,90],"help":[31],"in":[32,125,137],"deciding":[33],"between":[34],"those":[35,62],"and":[36,46],"competing":[37],"predictions.":[38],"It":[39,99],"is":[40,58,100,113,166,168],"shown":[41,101],"that":[42,102,165],"for":[43,172],"high":[44],"at":[47],"large":[48,174],"heights,":[49],"variability":[51,83],"moment":[53],"over":[55],"adjacent":[56],"intervals":[57,63],"substantial,":[59],"even":[60],"when":[61],"long,":[65],"as":[66,68,132,134],"long":[67,122],"a":[69],"block":[70],"containing":[71],"$10^9$":[72],"zeros":[73],"near":[74],"zero":[75],"number":[76],"$10^{23}$.":[77],"More":[78],"than":[79],"anything":[80],"else,":[81],"illustrates":[84],"limits":[86],"what":[88],"one":[89],"learn":[91],"about":[92],"from":[96],"numerical":[97,160],"evidence.":[98],"rate":[104],"decline":[106],"extreme":[108],"modeled":[114],"relatively":[115],"well":[116,133],"power":[118],"laws.":[119],"Also,":[120],"some":[121],"range":[123],"correlations":[124],"second":[130],"moment,":[131,144],"asymptotic":[135],"oscillations":[136],"shifted":[142],"fourth":[143],"found.":[146],"described":[149],"here":[150],"relied":[151],"several":[153],"representations":[154],"function.":[158],"comparison":[161],"their":[163],"effectiveness":[164],"presented":[167],"independent":[170],"interest,":[171],"future":[173],"scale":[175],"computations.":[176]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}
