{"id":"https://openalex.org/W7225638910","doi":"https://doi.org/10.5281/zenodo.24068306","title":"On the Spectral Localization and Adelic Energy Convexity of the Riemann Zeta Function","display_name":"On the Spectral Localization and Adelic Energy Convexity of the Riemann Zeta Function","publication_year":2026,"publication_date":"2026-11-09","ids":{"openalex":"https://openalex.org/W7225638910","doi":"https://doi.org/10.5281/zenodo.24068306"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24068306","doi":"https://doi.org/10.5281/zenodo.24068306","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24068306","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.24068306","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5161327594","display_name":"Sylvaunte Warren","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Warren, Sylvaunte","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5161327594"],"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.00019999999494757503,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/riemann-zeta-function","display_name":"Riemann zeta function","score":0.9470000267028809},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.8420000076293945},{"id":"https://openalex.org/keywords/nontrivial-zeros","display_name":"non-trivial zeros","score":0.8939999938011169},{"id":"https://openalex.org/keywords/spectral-localization","display_name":"spectral localization","score":0.7540000081062317},{"id":"https://openalex.org/keywords/berry-keating-operator","display_name":"Berry-Keating operator","score":0.9240000247955322},{"id":"https://openalex.org/keywords/self-adjointness","display_name":"self-adjointness","score":0.8999999761581421},{"id":"https://openalex.org/keywords/friedrichs-extension","display_name":"Friedrichs extension","score":0.9700000286102295},{"id":"https://openalex.org/keywords/dirichlet-polynomials","display_name":"Dirichlet polynomials","score":0.9020000100135803},{"id":"https://openalex.org/keywords/weighted-sobolev-spaces","display_name":"weighted Sobolev spaces","score":0.7509999871253967}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8590999841690063},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.6958000063896179},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5638999938964844},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.5059000253677368},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.47909998893737793},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.47099998593330383},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.4577000141143799},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.4546999931335449},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.4471000134944916},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.421999990940094},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4106999933719635},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.38519999384880066},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.3815000057220459},{"id":"https://openalex.org/C2780757906","wikidata":"https://www.wikidata.org/wiki/Q5276676","display_name":"Dilation (metric space)","level":2,"score":0.38119998574256897},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3765000104904175},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.34150001406669617},{"id":"https://openalex.org/C205979905","wikidata":"https://www.wikidata.org/wiki/Q215084","display_name":"Analytic function","level":2,"score":0.3215000033378601},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.3190000057220459},{"id":"https://openalex.org/C186934003","wikidata":"https://www.wikidata.org/wiki/Q1238449","display_name":"Polylogarithm","level":5,"score":0.30820000171661377},{"id":"https://openalex.org/C48902493","wikidata":"https://www.wikidata.org/wiki/Q2152235","display_name":"Riemann Xi function","level":3,"score":0.30630001425743103},{"id":"https://openalex.org/C161505775","wikidata":"https://www.wikidata.org/wiki/Q3240280","display_name":"Direct proof","level":2,"score":0.30469998717308044},{"id":"https://openalex.org/C55229022","wikidata":"https://www.wikidata.org/wiki/Q1789063","display_name":"L-function","level":3,"score":0.29319998621940613},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.2863999903202057},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.2800000011920929},{"id":"https://openalex.org/C2777478746","wikidata":"https://www.wikidata.org/wiki/Q5358910","display_name":"Elementary proof","level":2,"score":0.26570001244544983},{"id":"https://openalex.org/C96234433","wikidata":"https://www.wikidata.org/wiki/Q5280760","display_name":"Dirichlet's energy","level":4,"score":0.26499998569488525},{"id":"https://openalex.org/C27783845","wikidata":"https://www.wikidata.org/wiki/Q5421272","display_name":"Explicit formulae","level":2,"score":0.2547999918460846}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24068306","doi":"https://doi.org/10.5281/zenodo.24068306","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24068306","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.24068307","doi":"https://doi.org/10.5281/zenodo.24068307","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24068307","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.24068306","doi":"https://doi.org/10.5281/zenodo.24068306","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24068306","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7103651083","https://openalex.org/W7154496446","https://openalex.org/W7221538106","https://openalex.org/W7212166749","https://openalex.org/W6930819586","https://openalex.org/W7166507150","https://openalex.org/W7160432228","https://openalex.org/W7162433092","https://openalex.org/W7139964085","https://openalex.org/W7213674891"],"abstract_inverted_index":{"I":[0],"establish":[1],"a":[2,43],"self-contained,":[3],"classical":[4],"analytic":[5],"proof":[6],"that":[7,100],"all":[8],"non-trivial":[9],"zeros":[10],"of":[11,31,65],"the":[12,32,48,66,72,81],"completed":[13],"Riemann":[14],"zeta":[15],"function":[16],"\\xi(s)":[17],"satisfy":[18],"Re(s)":[19],"=":[20,37,78],"1/2.":[21],"The":[22],"architecture":[23],"unifies":[24],"three":[25],"primary":[26],"pillars:":[27],"(i)":[28],"essential":[29],"self-adjointness":[30],"Berry-Keating":[33],"dilation":[34],"operator":[35],"H":[36],"-i(x":[38],"d/dx":[39],"+":[40],"1/2)":[41],"on":[42],"dense":[44],"Mellin-Schwartz":[45],"domain":[46],"in":[47],"weighted":[49],"Sobolev":[50],"space":[51],"W^{1,2}(R^+,":[52],"dx/x)":[53],"via":[54],"Friedrichs":[55],"extension":[56],"and":[57,85,92],"boundary":[58],"concomitant":[59],"vanishing;":[60],"(ii)":[61],"strict":[62],"second-variation":[63],"positivity":[64],"logarithmic":[67],"derivative":[68],"energy":[69],"functional":[70],"across":[71],"idele":[73],"group":[74],"A_Q^\\times,":[75],"designating":[76],"\\sigma":[77],"1/2":[79],"as":[80],"unique":[82],"global":[83],"minimum;":[84],"(iii)":[86],"explicit":[87],"Tur\u00e1n-type":[88],"power":[89],"sum":[90],"bounds":[91],"Dirichlet":[93],"polynomial":[94],"mean-square":[95],"variance":[96],"estimates":[97],"O(T":[98],"N^{2\\delta})":[99],"rule":[101],"out":[102],"off-axis":[103],"zero":[104],"migration.":[105]},"counts_by_year":[],"updated_date":"2026-11-11T12:16:26.678958","created_date":"2026-11-10T00:00:00"}
