{"id":"https://openalex.org/W7225573370","doi":"https://doi.org/10.5281/zenodo.24055762","title":"Conductor decomposition of pair-count variance at fixed modulus: the c_pair(q) problem","display_name":"Conductor decomposition of pair-count variance at fixed modulus: the c_pair(q) problem","publication_year":2026,"publication_date":"2026-11-08","ids":{"openalex":"https://openalex.org/W7225573370","doi":"https://doi.org/10.5281/zenodo.24055762"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.24055762","doi":"https://doi.org/10.5281/zenodo.24055762","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24055762","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.24055762","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5105939703","display_name":"Robert Miller","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Miller, Robert","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0009-0004-5921-9557","affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5105939703"],"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":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":1.0,"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"}},{"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"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.0,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/twin-prime-conjecture","display_name":"twin prime conjecture","score":0.6959999799728394},{"id":"https://openalex.org/keywords/dirichlet-l-functions","display_name":"Dirichlet L-functions","score":0.8709999918937683},{"id":"https://openalex.org/keywords/zeros-of-l-functions","display_name":"zeros of L-functions","score":0.8429999947547913},{"id":"https://openalex.org/keywords/scale-invariance","display_name":"scale invariance","score":0.7229999899864197},{"id":"https://openalex.org/keywords/character-sums","display_name":"character sums","score":0.3840000033378601},{"id":"https://openalex.org/keywords/prime-number-theory","display_name":"prime number theory","score":0.3140000104904175}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7876999974250793},{"id":"https://openalex.org/C34800285","wikidata":"https://www.wikidata.org/wiki/Q5159395","display_name":"Conductor","level":2,"score":0.7494000196456909},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.5989999771118164},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.565500020980835},{"id":"https://openalex.org/C2777831296","wikidata":"https://www.wikidata.org/wiki/Q12518","display_name":"Tower","level":2,"score":0.4514999985694885},{"id":"https://openalex.org/C2778775528","wikidata":"https://www.wikidata.org/wiki/Q5135432","display_name":"Closing (real estate)","level":2,"score":0.38940000534057617},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3630000054836273},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.36169999837875366},{"id":"https://openalex.org/C121089165","wikidata":"https://www.wikidata.org/wiki/Q6889796","display_name":"Moduli","level":2,"score":0.3598000109195709},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3504999876022339},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.3416000008583069},{"id":"https://openalex.org/C154226666","wikidata":"https://www.wikidata.org/wiki/Q40089","display_name":"Brick","level":2,"score":0.3314000070095062},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.31150001287460327},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3077000081539154},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3066999912261963},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.29100000858306885},{"id":"https://openalex.org/C146786541","wikidata":"https://www.wikidata.org/wiki/Q157002","display_name":"Equilateral triangle","level":2,"score":0.289000004529953},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.28839999437332153},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.2603999972343445},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.25920000672340393},{"id":"https://openalex.org/C2779760435","wikidata":"https://www.wikidata.org/wiki/Q5396169","display_name":"Minor (academic)","level":2,"score":0.25870001316070557}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.5281/zenodo.24055762","doi":"https://doi.org/10.5281/zenodo.24055762","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24055762","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.24055763","doi":"https://doi.org/10.5281/zenodo.24055763","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24055763","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.24055762","doi":"https://doi.org/10.5281/zenodo.24055762","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.24055762","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/W7225579535","https://openalex.org/W2199517505","https://openalex.org/W7099805259","https://openalex.org/W7133200154","https://openalex.org/W2103045117","https://openalex.org/W7125789724","https://openalex.org/W3167972534","https://openalex.org/W2331879762","https://openalex.org/W1576436569","https://openalex.org/W2621243984"],"abstract_inverted_index":{"The":[0,75,199],"companion":[1],"paper":[2,29],"(DOI:":[3],"10.5281/zenodo.24055465)":[4],"established":[5],"that":[6,186],"prime-class":[7],"variance":[8,22,151],"K_p":[9],"is":[10,24,88,145,216],"classical":[11],"(Rubinstein\u2013Sarnak,":[12],"1/log":[13],"x":[14],"decay,":[15],"verified":[16],"at":[17,90,114,181],"three":[18,115],"moduli)":[19],"while":[20,92],"pair-class":[21],"K_K":[23],"scale-invariant":[25],"and":[26,40,51,141],"unexplained.":[27],"This":[28],"attacks":[30],"the":[31,37,45,66,69,123,158,169,204],"open":[32],"problem:":[33],"which":[34],"characters":[35],"carry":[36],"pair":[38,63,150],"variance,":[39],"does":[41,79,192],"it":[42],"relate":[43],"to":[44,96],"L-function":[46,197],"zero":[47,160],"spectrum?":[48],"Three":[49],"experiments":[50],"a":[52,146],"two-modulus":[53],"correlation":[54,156],"test":[55],"yield:":[56],"(1)":[57],"K_K's":[58],"scale-invariance":[59],"survives":[60],"\u039b\u039b-weighting":[61],"(the":[62],"analogue":[64],"of":[65],"\u03c8-test),":[67],"closing":[68],"last":[70],"bookkeeping":[71],"escape":[72],"hatch.":[73],"(2)":[74],"primorial":[76,236],"tower":[77],"recurrence":[78],"not":[80,106,193],"close":[81],"over":[82],"single":[83,209],"primes":[84],"\u2014":[85,207,215],"standalone":[86],"K_K\u00b2(p)":[87],"flat":[89],"~0.38":[91],"fibre":[93],"predictions":[94],"climb":[95],"0.51\u20130.74,":[97],"proving":[98],"c_pair":[99],"must":[100],"be":[101],"built":[102],"from":[103],"conductor":[104,229],"families,":[105],"prime":[107],"factors.":[108],"(3)":[109],"A":[110],"Parseval-exact":[111],"conductor-family":[112],"decomposition":[113],"moduli":[116],"(q":[117],"=":[118,143,163,173,179,183,189],"2310,":[119],"30030,":[120],"510510)":[121],"shows":[122,153],"highest-conductor":[124],"family":[125],"dominates":[126],"(63%":[127],"\u2192":[128,130,137,139],"57%":[129],"51%),":[131],"pure-prime":[132],"conductors":[133],"vanish":[134],"combinatorially":[135],"(5.4%":[136],"0.4%":[138],"0.04%),":[140],"p":[142],"3":[144],"spectator.":[147],"(4)":[148],"Per-character":[149],"|D'(\u03c7)|\u00b2":[152],"no":[154,208,212],"meaningful":[155],"with":[157],"single-character":[159],"sums":[161],"c(\u03c7)":[162],"\u03a3_\u03b3":[164],"1/(1/4":[165],"+":[166],"\u03b3\u00b2)":[167],"in":[168],"admissible-class":[170],"convention":[171],"(r":[172],"0.063,":[174],"r\u00b2":[175],"<":[176],"0.4%,":[177],"z":[178],"4.80":[180],"n":[182],"6),":[184],"confirming":[185],"E\u2082(x,":[187],"\u03c7)":[188],"\u03a3":[190],"\u039b(n)\u039b(n+h)\u03c7(n)":[191],"factor":[194],"through":[195],"individual":[196],"zeros.":[198],"brick":[200],"wall":[201],"predicted":[202],"by":[203,219],"Goldston\u2013Montgomery":[205],"theory":[206],"governing":[210],"L-function,":[211],"E\u2082":[213],"zero-sum":[214],"now":[217],"backed":[218],"data.":[220],"###":[221],"Keywordsprime":[222],"number":[223],"theory;":[224],"twin":[225],"primes;":[226],"Dirichlet":[227],"L-functions;":[228],"decomposition;":[230],"pair-correlation":[231],"variance;":[232],"Goldston-Montgomery;":[233],"admissible":[234],"classes;":[235],"modulus;":[237],"scale":[238],"invariance":[239]},"counts_by_year":[],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2026-11-09T00:00:00"}
