{"id":"https://openalex.org/W7223678604","doi":"https://doi.org/10.5281/zenodo.23660401","title":"Odd Zeta Values in QED: The Loop Order Chooses the Weight (P5)","display_name":"Odd Zeta Values in QED: The Loop Order Chooses the Weight (P5)","publication_year":2026,"publication_date":"2026-10-26","ids":{"openalex":"https://openalex.org/W7223678604","doi":"https://doi.org/10.5281/zenodo.23660401"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.23660401","doi":"https://doi.org/10.5281/zenodo.23660401","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23660401","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","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.23660401","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5132603461","display_name":"Thomas Krause","orcid":"https://orcid.org/0009-0004-3867-9941","observed_orcids":["https://orcid.org/0009-0004-3867-9941"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Krause, Thomas","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0004-3867-9941","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5132603461"],"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9506999850273132,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9506999850273132,"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/T10048","display_name":"Particle physics theoretical and experimental studies","score":0.026499999687075615,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy 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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.008700000122189522,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/odd-zeta-values","display_name":"odd zeta values","score":0.824999988079071},{"id":"https://openalex.org/keywords/electron-anomalous-magnetic-moment","display_name":"electron anomalous magnetic moment","score":0.9279999732971191},{"id":"https://openalex.org/keywords/quantum-electrodynamics","display_name":"quantum electrodynamics","score":0.4000000059604645},{"id":"https://openalex.org/keywords/zeta-function-values","display_name":"zeta function values","score":0.5059999823570251},{"id":"https://openalex.org/keywords/clausen-function","display_name":"Clausen function","score":0.5640000104904175},{"id":"https://openalex.org/keywords/massless-phi-4-theory","display_name":"massless phi^4 theory","score":0.800000011920929},{"id":"https://openalex.org/keywords/catalan-numbers","display_name":"Catalan numbers","score":0.6819999814033508},{"id":"https://openalex.org/keywords/period","display_name":"period","score":0.5600000023841858},{"id":"https://openalex.org/keywords/eta-function","display_name":"eta function","score":0.6880000233650208},{"id":"https://openalex.org/keywords/fine-structure-constant","display_name":"fine-structure constant","score":0.8019999861717224},{"id":"https://openalex.org/keywords/feynman-parameters","display_name":"Feynman parameters","score":0.6439999938011169}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8173999786376953},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5160999894142151},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5012999773025513},{"id":"https://openalex.org/C46875033","wikidata":"https://www.wikidata.org/wiki/Q1244890","display_name":"Rational number","level":2,"score":0.4909000098705292},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4221000075340271},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.41100001335144043},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.3950999975204468},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.38449999690055847},{"id":"https://openalex.org/C184670325","wikidata":"https://www.wikidata.org/wiki/Q512604","display_name":"Loop (graph theory)","level":2,"score":0.37059998512268066},{"id":"https://openalex.org/C188370112","wikidata":"https://www.wikidata.org/wiki/Q173091","display_name":"Transcendental number","level":2,"score":0.3686999976634979},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3598000109195709},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.3492000102996826},{"id":"https://openalex.org/C2777151079","wikidata":"https://www.wikidata.org/wiki/Q141160","display_name":"Parity (physics)","level":2,"score":0.34470000863075256},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.3402000069618225},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.3163999915122986},{"id":"https://openalex.org/C113429393","wikidata":"https://www.wikidata.org/wiki/Q49008","display_name":"Prime number","level":2,"score":0.3138999938964844},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.3122999966144562},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.31209999322891235},{"id":"https://openalex.org/C174072685","wikidata":"https://www.wikidata.org/wiki/Q1667469","display_name":"Prime power","level":3,"score":0.3041999936103821},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.30230000615119934},{"id":"https://openalex.org/C28581250","wikidata":"https://www.wikidata.org/wiki/Q13407133","display_name":"Harmonic number","level":3,"score":0.2980000078678131},{"id":"https://openalex.org/C34718186","wikidata":"https://www.wikidata.org/wiki/Q209875","display_name":"Binomial coefficient","level":2,"score":0.28290000557899475},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.27970001101493835},{"id":"https://openalex.org/C127843967","wikidata":"https://www.wikidata.org/wiki/Q1554628","display_name":"Cyclotomic field","level":2,"score":0.2775000035762787},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.27219998836517334},{"id":"https://openalex.org/C139676723","wikidata":"https://www.wikidata.org/wiki/Q1193832","display_name":"Sign (mathematics)","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2680000066757202},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.2648000121116638},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.26170000433921814}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.23660401","doi":"https://doi.org/10.5281/zenodo.23660401","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23660401","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.23660402","doi":"https://doi.org/10.5281/zenodo.23660402","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23660402","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.23660401","doi":"https://doi.org/10.5281/zenodo.23660401","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.23660401","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/W7159825699","https://openalex.org/W7155088977","https://openalex.org/W7159045929","https://openalex.org/W2974116394","https://openalex.org/W7138871701","https://openalex.org/W2019225253","https://openalex.org/W2906293334","https://openalex.org/W7155061562","https://openalex.org/W6885149122","https://openalex.org/W4401251985"],"abstract_inverted_index":{"Summary:":[0],"The":[1,246,270,292],"anomalous":[2],"magnetic":[3,309,390],"moment":[4,310,391],"of":[5,133,157,237,248,266,331,349,380,392],"the":[6,57,60,64,67,71,77,82,86,92,99,104,108,116,146,149,174,192,198,201,209,217,231,238,249,257,260,263,282,286,302,308,325,328,335,338,344,350,364,369,377,381,386,393],"electron":[7],"is":[8,43,95,101,114,122,194,244,273,294,305,323,327],"a":[9,221,225],"power":[10],"series":[11],"a\u2091":[12],"=":[13,168,184,190],"\u03a3\u2099":[14],"A\u2099(\u03b1/\u03c0)\u207f":[15],"whose":[16,383],"coefficients":[17,156,333],"are":[18,130],"known":[19,90,332],"exactly":[20,241],"up":[21],"to":[22,314,367],"four":[23,40],"loops.":[24,41],"They":[25],"contain":[26],"\u03b6(3)":[27],"from":[28,33,164,307,355],"two":[29,171,352],"loops":[30,35,370],"on,":[31],"\u03b6(5)":[32],"three":[34],"on":[36],"and":[37,63,70,103,135,180,196,216,256,262,288,311,317,334,347],"\u03b6(7)":[38],"at":[39,53,96,119,138],"It":[42],"not":[44,274,371],"usually":[45],"asked":[46],"why":[47],"odd":[48,124],"zeta":[49,125,395,397,400],"values":[50,69,128],"appear":[51],"here":[52],"all,":[54],"while":[55],"in":[56,88,142,197,205,337],"Casimir":[58],"effect,":[59],"blackbody":[61],"law":[62],"Bose":[65,261],"gas":[66],"even":[68,127],"Gamma":[72],"factors":[73],"dominate.":[74],"We":[75],"make":[76],"arithmetic":[78,329],"bookkeeping":[79],"explicit.":[80],"First,":[81],"loop":[83,250],"order":[84,121],"chooses":[85],"weight:":[87],"every":[89],"coefficient":[91],"transcendental":[93],"weight":[94,106,140,147,214],"most":[97],"2n\u22121,":[98,169],"bound":[100],"attained,":[102],"top":[105],"contains":[107],"single":[109],"value":[110],"\u03b6(2n\u22121).":[111],"Since":[112],"2n\u22121":[113],"odd,":[115],"new":[117,321],"constant":[118,272,412],"each":[120],"an":[123],"value;":[126],"\u03b6(2k)":[129],"rational":[131,155],"multiples":[132],"\u03c0\u00b2\u1d4f":[134],"enter":[136],"only":[137,148],"lower":[139],"or":[141],"products.":[143],"Second,":[144],"beyond":[145],"prime":[150,175,239],"2":[151,240,300],"enters:":[152],"all":[153],"115":[154],"Laporta's":[158],"four-loop":[159],"result":[160],"have":[161],"denominators":[162],"built":[163],"primes":[165],"\u2264":[166],"7":[167],"with":[170,213,230],"exceptions":[172],"carrying":[173],"11.":[176],"Both":[177],"multiply":[178],"Cl\u2086(\u03c0/3),":[179],"we":[181,276],"prove":[182],"Cl\u2082\u2098(2\u03c0/3)":[183],"Cl\u2082\u2098(\u03c0/3)/(1":[185],"+":[186],"2^(1\u22122m));":[187],"for":[188,296],"m":[189],"3":[191],"factor":[193,233],"32/33,":[195],"basis":[199],"Cl\u2086(2\u03c0/3)":[200],"11":[202],"disappears.":[203],"Third,":[204],"massless":[206],"\u03c6\u2074":[207],"theory":[208],"same":[210],"rule":[211],"holds":[212],"2\u2113\u22123,":[215],"zig-zag":[218],"graphs":[219,354],"give":[220],"proved":[222],"closed":[223],"form:":[224],"Catalan":[226],"number":[227,251,297,384],"times":[228],"\u03b6(2\u2113\u22123),":[229],"Euler":[232],"1":[234],"\u2212":[235],"2^(4\u22122\u2113)":[236],"when":[242],"\u2113":[243],"odd.":[245],"parity":[247],"thus":[252],"decides":[253],"between":[254,285],"\u03b6":[255],"alternating":[258],"\u03b7,":[259],"Fermi":[264],"side":[265],"our":[267],"earlier":[268],"papers.":[269],"fine-structure":[271],"derived;":[275],"record":[277],"its":[278],"present":[279],"status,":[280],"including":[281],"5.5\u03c3":[283],"tension":[284],"rubidium":[287],"caesium":[289],"recoil":[290],"measurements.":[291],"paper":[293],"written":[295],"theorists:":[298],"Section":[299],"explains":[301],"physics":[303,322],"that":[304],"needed,":[306],"Feynman":[312],"parameters":[313],"periods,":[315],"weights":[316],"graph":[318],"polynomials.":[319,358],"No":[320],"claimed;":[324],"contribution":[326],"reading":[330],"checks":[336],"companion":[339],"code,":[340],"which":[341],"also":[342],"recomputes":[343],"periods":[345],"6\u03b6(3)":[346],"20\u03b6(5)":[348],"first":[351],"wheel":[353],"their":[356],"Kirchhoff":[357],"A":[359],"final":[360],"section":[361],"proposes,":[362],"as":[363,372,376],"author's":[365],"hypothesis,":[366],"read":[368],"vacuum":[373],"fluctuations":[374],"but":[375],"independent":[378],"cycles":[379],"graphs,":[382],"fixes":[385],"weight.":[387],"quantum":[388],"electrodynamicsanomalous":[389],"electronRiemann":[394],"functionodd":[396],"valuestranscendental":[398],"weightmultiple":[399],"valuesperiodsFeynman":[401],"integralsKirchhoff":[402],"polynomialgraph":[403],"polynomialsphi^4":[404],"theoryzig-zag":[405],"graphsCatalan":[406],"numbersClausen":[407],"functionDirichlet":[408],"eta":[409],"functionEuler":[410],"productfine-structure":[411]},"counts_by_year":[],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2026-10-27T00:00:00"}
