{"id":"https://openalex.org/W7223010804","doi":"https://doi.org/10.48550/arxiv.2610.26575","title":"Surfaces Associated to Zeros of Automorphic $L$-functions","display_name":"Surfaces Associated to Zeros of Automorphic $L$-functions","publication_year":2026,"publication_date":"2026-10-19","ids":{"openalex":"https://openalex.org/W7223010804","doi":"https://doi.org/10.48550/arxiv.2610.26575"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.26575","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.26575","pdf_url":"https://arxiv.org/pdf/2610.26575","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/2610.26575","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029156042","display_name":"Debmalya Basak","orcid":"https://orcid.org/0000-0001-5262-3478","observed_orcids":["https://orcid.org/0000-0001-5262-3478"]},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Basak, Debmalya","raw_affiliation_strings":["DEPARTMENT OF MATHEMATICS , UNIVERSITY OF ILLINOIS URBANA-CHAMPAIGN , ALTGELD HALL , 1409 W. GREEN STREET , URBANA , IL , 61801 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DEPARTMENT OF MATHEMATICS , UNIVERSITY OF ILLINOIS URBANA-CHAMPAIGN , ALTGELD HALL , 1409 W. GREEN STREET , URBANA , IL , 61801 , USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050118236","display_name":"Cruz Castillo","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Castillo, Cruz","raw_affiliation_strings":["DEPARTMENT OF MATHEMATICS , UNIVERSITY OF ILLINOIS URBANA-CHAMPAIGN , ALTGELD HALL , 1409 W. GREEN STREET , URBANA , IL , 61801 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DEPARTMENT OF MATHEMATICS , UNIVERSITY OF ILLINOIS URBANA-CHAMPAIGN , ALTGELD HALL , 1409 W. GREEN STREET , URBANA , IL , 61801 , USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044281552","display_name":"Alexandru Zaharescu","orcid":"https://orcid.org/0000-0001-5587-9938","observed_orcids":["https://orcid.org/0000-0001-5587-9938"]},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]},{"id":"https://openalex.org/I4405262991","display_name":"IMAR - Institutul de Matematic\u0103 \u201eSimion Stoilow\u201d al Academiei Rom\u00e2ne","ror":"https://ror.org/0122mh736","country_code":"RO","type":"education","lineage":["https://openalex.org/I4405262991","https://openalex.org/I58077936"]}],"countries":["RO","US"],"is_corresponding":false,"raw_author_name":"Zaharescu, Alexandru","raw_affiliation_strings":["AND SIMION STOILOW INSTITUTE OF MATHEMATICS OF THE ROMANIAN ACADEMY , P. O. BOX 1-764 , RO-014700 BUCHAREST , ROMANIA","DEPARTMENT OF MATHEMATICS , UNIVERSITY OF ILLINOIS URBANA-CHAMPAIGN , ALTGELD HALL , 1409 W. GREEN STREET , URBANA , IL , 61801 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"AND SIMION STOILOW INSTITUTE OF MATHEMATICS OF THE ROMANIAN ACADEMY , P. O. BOX 1-764 , RO-014700 BUCHAREST , ROMANIA","institution_ids":["https://openalex.org/I4405262991"]},{"raw_affiliation_string":"DEPARTMENT OF MATHEMATICS , UNIVERSITY OF ILLINOIS URBANA-CHAMPAIGN , ALTGELD HALL , 1409 W. GREEN STREET , URBANA , IL , 61801 , USA","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":0.9976000189781189,"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":0.9976000189781189,"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":0.0006000000284984708,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.0005000000237487257,"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/automorphic-l-functions","display_name":"automorphic L-functions","score":0.9869999885559082},{"id":"https://openalex.org/keywords/zeros-of-l-functions","display_name":"zeros of L-functions","score":0.9760000109672546},{"id":"https://openalex.org/keywords/pairwise-correlations","display_name":"two-particle correlations","score":0.8510000109672546},{"id":"https://openalex.org/keywords/triple-correlation","display_name":"triple correlation","score":0.875},{"id":"https://openalex.org/keywords/level-correlations","display_name":"level correlations","score":0.7689999938011169},{"id":"https://openalex.org/keywords/riemann-hypothesis","display_name":"Riemann hypothesis","score":0.7699999809265137},{"id":"https://openalex.org/keywords/laplace-distribution","display_name":"Laplace distribution","score":0.9309999942779541},{"id":"https://openalex.org/keywords/chi-square-distribution","display_name":"chi-square distribution","score":0.9929999709129333},{"id":"https://openalex.org/keywords/phase-transitions","display_name":"phase transitions","score":0.9269999861717224}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7365000247955322},{"id":"https://openalex.org/C199479865","wikidata":"https://www.wikidata.org/wiki/Q205966","display_name":"Riemann hypothesis","level":2,"score":0.6182000041007996},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.49219998717308044},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.4702000021934509},{"id":"https://openalex.org/C18556879","wikidata":"https://www.wikidata.org/wiki/Q753035","display_name":"Riemann surface","level":2,"score":0.4474000036716461},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43560001254081726},{"id":"https://openalex.org/C132817261","wikidata":"https://www.wikidata.org/wiki/Q1134435","display_name":"Automorphic form","level":2,"score":0.41940000653266907},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.4081000089645386},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4068000018596649},{"id":"https://openalex.org/C48902493","wikidata":"https://www.wikidata.org/wiki/Q2152235","display_name":"Riemann Xi function","level":3,"score":0.37630000710487366},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.3714999854564667},{"id":"https://openalex.org/C202434901","wikidata":"https://www.wikidata.org/wiki/Q4826697","display_name":"Automorphic L-function","level":3,"score":0.2709999978542328},{"id":"https://openalex.org/C154483964","wikidata":"https://www.wikidata.org/wiki/Q825857","display_name":"Riemann sphere","level":3,"score":0.2702000141143799},{"id":"https://openalex.org/C27783845","wikidata":"https://www.wikidata.org/wiki/Q5421272","display_name":"Explicit formulae","level":2,"score":0.25429999828338623},{"id":"https://openalex.org/C112468886","wikidata":"https://www.wikidata.org/wiki/Q5535485","display_name":"Geometric function theory","level":3,"score":0.2531999945640564},{"id":"https://openalex.org/C2779664074","wikidata":"https://www.wikidata.org/wiki/Q3518405","display_name":"Terminal (telecommunication)","level":2,"score":0.2515000104904175},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.26575","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.26575","pdf_url":"https://arxiv.org/pdf/2610.26575","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.2610.26575","doi":"https://doi.org/10.48550/arxiv.2610.26575","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.26575","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.26575","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.26575","pdf_url":"https://arxiv.org/pdf/2610.26575","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":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306151","display_name":"Alfred P. Sloan Foundation","ror":"https://ror.org/052csg198"},{"id":"https://openalex.org/F4320309292","display_name":"Princeton University","ror":"https://ror.org/00hx57361"},{"id":"https://openalex.org/F4320332222","display_name":"University of Illinois at Urbana-Champaign","ror":"https://ror.org/047426m28"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7223010804.pdf","grobid_xml":"https://content.openalex.org/works/W7223010804.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W7077053945","https://openalex.org/W7203614468"],"related_works":["https://openalex.org/W7025662493","https://openalex.org/W2568845387","https://openalex.org/W2182280203","https://openalex.org/W1805051590","https://openalex.org/W295971711","https://openalex.org/W2559667753","https://openalex.org/W2069023986","https://openalex.org/W2025091605","https://openalex.org/W576373948","https://openalex.org/W3193676646"],"abstract_inverted_index":{"Assuming":[0],"the":[1,13,37,43],"Riemann":[2,14],"Hypothesis,":[3],"Montgomery":[4],"established":[5],"results":[6,22],"concerning":[7],"pair":[8,46],"correlation":[9],"of":[10,12,39,45],"zeros":[11,38],"zeta":[15],"function.":[16],"Rudnick":[17],"and":[18,26,64],"Sarnak":[19],"extended":[20],"these":[21,48,60],"to":[23,36],"automorphic":[24,40],"$L$-functions":[25],"all":[27],"level":[28],"correlations.":[29],"We":[30],"discover":[31],"additional":[32],"geometric":[33],"structures":[34,49,61],"associated":[35],"$L$-functions.":[41],"In":[42],"case":[44],"correlation,":[47,59],"form":[50],"certain":[51],"surfaces":[52],"which":[53],"display":[54],"Gaussian":[55],"behavior.":[56],"For":[57],"triple":[58],"exhibit":[62],"Laplace":[63],"Chi-squared":[65],"distributions,":[66],"revealing":[67],"an":[68],"unexpected":[69],"phase":[70],"transition.":[71]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-10-21T00:00:00"}