{"id":"https://openalex.org/W7222998064","doi":"https://doi.org/10.13140/rg.2.2.19482.20163","title":"Upper Bounds on the De Bruijn-Newman constant for Dirichlet L-functions with primitive real-valued characters","display_name":"Upper Bounds on the De Bruijn-Newman constant for Dirichlet L-functions with primitive real-valued characters","publication_year":2026,"publication_date":"2026-10-19","ids":{"openalex":"https://openalex.org/W7222998064","doi":"https://doi.org/10.13140/rg.2.2.19482.20163"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.27343","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.27343","pdf_url":"https://arxiv.org/pdf/2610.27343","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/2610.27343","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159129971","display_name":"Ricardo Freire","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ricardo Freire","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045765589","display_name":"Cristian Gonz\u00e1lez-Riquelme","orcid":"https://orcid.org/0000-0002-6614-8003","observed_orcids":["https://orcid.org/0000-0002-6614-8003"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cristian Gonz\u00e1lez-Riquelme","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5159125759","display_name":"Claudio Mu\u00f1oz","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Claudio Mu\u00f1oz","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039300414","display_name":"Felipe Poblete","orcid":"https://orcid.org/0009-0004-1219-3839","observed_orcids":["https://orcid.org/0009-0004-1219-3839"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Felipe Poblete","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5159118042","display_name":"Vicente Salinas","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Vicente Salinas","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/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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.0,"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":0.0,"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/de-bruijn-newman-constant","display_name":"de Bruijn-Newman constant","score":0.984000027179718},{"id":"https://openalex.org/keywords/dirichlet-l-functions","display_name":"Dirichlet L-functions","score":0.9049999713897705},{"id":"https://openalex.org/keywords/generalized-riemann-hypothesis","display_name":"generalized Riemann hypothesis","score":0.921999990940094},{"id":"https://openalex.org/keywords/backward-heat-equation","display_name":"backward heat equation","score":0.7509999871253967}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6671000123023987},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5999000072479248},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5026999711990356},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.450300008058548},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3353999853134155},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.2971999943256378},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.2883000075817108},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.25690001249313354},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.25369998812675476},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.23409999907016754}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2610.27343","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.27343","pdf_url":"https://arxiv.org/pdf/2610.27343","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.2610.27343","doi":"https://doi.org/10.48550/arxiv.2610.27343","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.27343","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"},{"id":"doi:10.13140/rg.2.2.19482.20163","doi":"https://doi.org/10.13140/rg.2.2.19482.20163","is_oa":false,"landing_page_url":"https://doi.org/10.13140/rg.2.2.19482.20163","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.27343","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.27343","pdf_url":"https://arxiv.org/pdf/2610.27343","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7222998064.pdf","grobid_xml":"https://content.openalex.org/works/W7222998064.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W824398093","https://openalex.org/W1556596029","https://openalex.org/W1632975364","https://openalex.org/W2000265435","https://openalex.org/W2002795182","https://openalex.org/W2008814803","https://openalex.org/W2034345839","https://openalex.org/W2093285600","https://openalex.org/W2112068204","https://openalex.org/W2123875891","https://openalex.org/W2135286272","https://openalex.org/W2163624185","https://openalex.org/W2281218105","https://openalex.org/W2329471412","https://openalex.org/W2552835512","https://openalex.org/W2940545432","https://openalex.org/W3016082228","https://openalex.org/W3018101995","https://openalex.org/W3213504679"],"related_works":["https://openalex.org/W2175186690","https://openalex.org/W2239241610","https://openalex.org/W7099704885","https://openalex.org/W4288364050","https://openalex.org/W7202128174","https://openalex.org/W7221781177","https://openalex.org/W2039017895","https://openalex.org/W1632975364","https://openalex.org/W4254906725","https://openalex.org/W2080252578"],"abstract_inverted_index":{"Let":[0],"$\u03c7_m$":[1],"be":[2,13],"a":[3,74,85],"primitive":[4,155],"real-valued":[5,156],"Dirichlet":[6,16,176],"character":[7,157],"of":[8,70,81,100,158,173,194,218],"conductor":[9,159,180],"$m\\ge3$,":[10],"let":[11,19],"$L(s)=L(s,\u03c7_m)$":[12],"the":[14,33,48,67,79,90,98,121,129,140,148,170,179,183,216],"associated":[15],"$L$-function,":[17],"and":[18,72,105,198],"$\u03be_L(s)$":[20],"denote":[21],"its":[22],"completed":[23],"form.":[24],"For":[25],"each":[26],"$t":[27,108],"\\in":[28,63],"\\mathbb":[29,64],"R,$":[30],"we":[31],"define":[32],"entire":[34],"function":[35],"\\[":[36,52],"H^L_t(z)":[37],":=":[38,54],"\\int_{-\\infty}^{\\infty}":[39],"e^{tu^2}\\,":[40],"\u03a6_L(u)\\,":[41],"e^{izu}\\,":[42],"du,":[43],"\\]":[44,59],"where":[45],"$\u03a6_L$":[46],"is":[47,118],"superexponentially":[49],"decaying":[50],"density":[51],"\u03a6_L(u)":[53],"\\frac{1}{2\u03c0}\\int_{-\\infty}^{\\infty}":[55],"\u03be_L\\!\\left(\\frac{1+is}{2}\\right)":[56],"e^{-isu}\\,":[57],"ds.":[58],"The":[60,111,167],"family":[61],"$\\{H_t^L\\}_{t":[62],"R}$":[65],"describes":[66],"heat-flow":[68],"evolution":[69],"$\u03be_L$":[71],"solves":[73],"backward":[75],"heat":[76],"equation.":[77],"By":[78],"work":[80],"Newman,":[82],"there":[83],"exists":[84],"finite":[86],"constant":[87],"$\u039b_L$,":[88],"called":[89],"generalized":[91],"de":[92,137],"Bruijn--Newman":[93],"constant,":[94],"such":[95],"that":[96,123],"all":[97],"zeros":[99,217],"$H_t^L$":[101],"are":[102],"real":[103],"if":[104,107],"only":[106],"\\ge":[109,134],"\u039b_L$.":[110],"Generalized":[112],"Riemann":[113],"Hypothesis":[114],"(GRH)":[115],"for":[116,153,215],"$L$":[117],"equivalent":[119],"to":[120,175],"assertion":[122],"$\u039b_L":[124,133,143],"\\le":[125,144],"0$.":[126],"Dobner":[127],"established":[128],"matching":[130],"lower":[131],"bound":[132,142,151],"0$,":[135],"while":[136],"Bruijn":[138],"proved":[139],"upper":[141],"\\tfrac12$.":[145],"We":[146,186,202],"prove":[147],"unconditional":[149],"uniform":[150],"$\u039b_L\\le953/3200=0.2978125$":[152],"every":[154],"$3\\le":[160],"m\\le400$,":[161],"together":[162],"with":[163,190],"stronger":[164],"individual":[165],"bounds.":[166],"proof":[168],"extends":[169],"effective":[171],"approximation":[172],"Polymath":[174],"$L$-functions,":[177],"retaining":[178],"dependence":[181],"in":[182],"error":[184],"estimates.":[185],"combine":[187],"these":[188],"estimates":[189],"Platt's":[191],"numerical":[192],"verification":[193],"GRH":[195],"by":[196],"Platt":[197],"rigorous":[199],"interval":[200],"computations.":[201],"also":[203],"give":[204],"conditional":[205],"bounds":[206],"under":[207],"explicit":[208],"global":[209],"initial":[210],"zero-strip":[211],"hypotheses,":[212],"including":[213],"$|\\operatorname{Im}z|\\le3/4$":[214],"$H_0^L$.":[219]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-10-21T00:00:00"}