{"id":"https://openalex.org/W2964474121","doi":null,"title":"Analytic Continuation of the Zeta Function Violates the Law of Non-Contradiction (LNC)","display_name":"Analytic Continuation of the Zeta Function Violates the Law of Non-Contradiction (LNC)","publication_year":2019,"publication_date":"2019-07-01","ids":{"openalex":"https://openalex.org/W2964474121","mag":"2964474121"},"language":"en","primary_location":{"id":"mag:2964474121","doi":null,"is_oa":false,"landing_page_url":"https://vixra.org/pdf/1907.0463v1.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S2883122597","display_name":"viXra","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"viXra","raw_type":null},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080934429","display_name":"Ayal Sharon","orcid":"https://orcid.org/0000-0002-5690-6181","observed_orcids":["https://orcid.org/0000-0002-5690-6181"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ayal Sharon","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-5690-6181","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5080934429"],"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":0.9765999913215637,"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":0.9765999913215637,"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.010999999940395355,"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/T12170","display_name":"History and Theory of Mathematics","score":0.0024999999441206455,"subfield":{"id":"https://openalex.org/subfields/1207","display_name":"History and Philosophy of Science"},"field":{"id":"https://openalex.org/fields/12","display_name":"Arts and Humanities"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/riemann-zeta-function","display_name":"Riemann zeta function","score":0.9959999918937683},{"id":"https://openalex.org/keywords/analytic-continuation","display_name":"analytic continuation","score":0.9909999966621399},{"id":"https://openalex.org/keywords/principle-of-non-contradiction","display_name":"principle of contradiction","score":0.9279999732971191},{"id":"https://openalex.org/keywords/cauchy-integral-theorem","display_name":"Cauchy's theorem","score":0.8489999771118164},{"id":"https://openalex.org/keywords/l-functions","display_name":"L-functions","score":0.8059999942779541},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.7720000147819519},{"id":"https://openalex.org/keywords/principle-of-explosion","display_name":"principle of explosion","score":0.7699999809265137},{"id":"https://openalex.org/keywords/intuitionistic-logic","display_name":"intuitionistic logic","score":0.75},{"id":"https://openalex.org/keywords/three-valued-logic","display_name":"ternary logic","score":0.8690000176429749},{"id":"https://openalex.org/keywords/paraconsistent-logic","display_name":"paraconsistent logic","score":0.6930000185966492},{"id":"https://openalex.org/keywords/law-of-excluded-middle","display_name":"law of excluded middle","score":0.609000027179718},{"id":"https://openalex.org/keywords/law-of-identity","display_name":"Law of Identity","score":0.9449999928474426}],"concepts":[{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.7991536855697632},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7487289309501648},{"id":"https://openalex.org/C151602998","wikidata":"https://www.wikidata.org/wiki/Q485287","display_name":"Analytic continuation","level":2,"score":0.7137339115142822},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.48711228370666504},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4751605689525604},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4167132079601288},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.358553946018219},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"mag:2964474121","doi":null,"is_oa":false,"landing_page_url":"https://vixra.org/pdf/1907.0463v1.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S2883122597","display_name":"viXra","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"viXra","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2903530165","https://openalex.org/W4394668781","https://openalex.org/W2792825188","https://openalex.org/W2971966010","https://openalex.org/W2788816558","https://openalex.org/W2965714545","https://openalex.org/W3156625358","https://openalex.org/W2788112650","https://openalex.org/W3084315925","https://openalex.org/W2999964257"],"abstract_inverted_index":{"The":[0],"Dirichlet":[1],"series":[2],"of":[3,30,40,71,74,78,83,91,101,107,123,134,137,140,150,161,166],"the":[4,31,48,76,81,84,89,99,105,115,124,135,141,151,162,167,202],"Zeta":[5,32,49,125,142,146,168,194],"function":[6,33,50,126,147],"was":[7],"long":[8],"ago":[9],"proven":[10],"to":[11,224],"be":[12],"divergent":[13,53],"throughout":[14,56],"half-plane":[15,57],"Re(s)":[16,58],"=<":[17,59],"1.":[18],"If":[19],"also":[20,103,199],"Riemann's":[21,120,145,193],"proposition":[22],"is":[23,35,51,148,196,206],"true,":[24],"that":[25,34,187,189,201,219],"there":[26],"exists":[27],"an":[28,190],"expression":[29],"convergent":[36,55],"at":[37,43,62],"all":[38,69,155,174],"values":[39],"s":[41,44,63],"(except":[42,61],"=":[45,64],"1),":[46],"then":[47],"both":[52],"and":[54,88,96,180],"1":[60],"1).":[65],"This":[66,170],"result":[67,171],"violates":[68,127],"three":[70],"Aristotle's":[72],"Laws":[73],"Thought:":[75],"Law":[77,82,90],"Identity":[79],"(LOI),":[80],"Excluded":[85],"Middle":[86],"(LEM),":[87],"Non-Contradition":[92],"(LNC).":[93],"In":[94,113],"classical":[95,211],"intuitionistic":[97,213],"logics,":[98],"violation":[100],"LNC":[102],"triggers":[104],"Principle":[106],"Explosion:":[108],"Ex":[109],"Contradictione":[110],"Quodlibet":[111],"(ECQ).":[112],"addition,":[114],"Hankel":[116],"contour":[117],"used":[118],"in":[119,210],"analytic":[121,138,164],"continuation":[122,139,165],"Cauchy's":[128],"integral":[129],"theorem,":[130],"providing":[131],"another":[132],"proof":[133],"invalidity":[136],"function.":[143,169],"Also,":[144],"one":[149],"L-functions,":[152],"which":[153],"are":[154,159],"invalid,":[156],"because":[157],"they":[158],"generalizations":[160],"invalid":[163],"renders":[172],"unsound":[173],"theorems":[175],"(e.g.":[176,182,192],"Modularity,":[177],"Fermat's":[178],"last)":[179],"conjectures":[181],"BSD,":[183],"Tate,":[184],"Hodge,":[185],"Yang-Mills)":[186],"assume":[188],"L-function":[191],"function)":[195],"valid.":[197],"We":[198],"show":[200],"Riemann":[203],"Hypothesis":[204],"(RH)":[205],"not":[207],"non-trivially":[208],"true":[209],"logic,":[212,214],"or":[215],"three-valued":[216],"logics":[217],"(3VLs)":[218],"assign":[220],"a":[221],"third":[222],"truth-value":[223],"paradoxes":[225],"(Bochvar's":[226],"3VL,":[227],"Priest's":[228],"LP).":[229]},"counts_by_year":[],"updated_date":"2025-10-10T17:16:08.811792","created_date":"2019-08-13T00:00:00"}
