{"id":"https://openalex.org/W4409410641","doi":"https://doi.org/10.1002/mana.12016","title":"Angular distribution toward the points of the neighbor\u2010flips modular curve seen by a fast moving observer","display_name":"Angular distribution toward the points of the neighbor\u2010flips modular curve seen by a fast moving observer","publication_year":2025,"publication_date":"2025-04-14","ids":{"openalex":"https://openalex.org/W4409410641","doi":"https://doi.org/10.1002/mana.12016"},"language":"en","primary_location":{"id":"doi:10.1002/mana.12016","doi":"https://doi.org/10.1002/mana.12016","is_oa":true,"landing_page_url":"https://doi.org/10.1002/mana.12016","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/mana.12016","source":{"id":"https://openalex.org/S73458468","display_name":"Mathematische Nachrichten","issn_l":"0025-584X","issn":["0025-584X","1522-2616"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematische Nachrichten","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/mana.12016","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Jack Anderson","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":"Jack Anderson","raw_affiliation_strings":["Department of Mathematics University of Illinois at Urbana\u2010Champaign  Urbana Illinois USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Illinois at Urbana\u2010Champaign  Urbana Illinois USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071408046","display_name":"Florin P. Boca","orcid":"https://orcid.org/0000-0002-2922-0547","observed_orcids":["https://orcid.org/0000-0002-2922-0547"]},"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":true,"raw_author_name":"Florin P. Boca","raw_affiliation_strings":["Department of Mathematics University of Illinois at Urbana\u2010Champaign  Urbana Illinois USA"],"raw_orcid":"https://orcid.org/0000-0002-2922-0547","affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Illinois at Urbana\u2010Champaign  Urbana Illinois USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015883769","display_name":"Cristian Cobeli","orcid":"https://orcid.org/0000-0003-1614-8280","observed_orcids":["https://orcid.org/0000-0003-1614-8280"]},"institutions":[{"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"],"is_corresponding":false,"raw_author_name":"Cristian Cobeli","raw_affiliation_strings":["\u201cSimion Stoilow\u201d Institute of Mathematics of the Romanian Academy  Bucharest Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u201cSimion Stoilow\u201d Institute of Mathematics of the Romanian Academy  Bucharest Romania","institution_ids":["https://openalex.org/I4405262991"]}]},{"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":"Alexandru Zaharescu","raw_affiliation_strings":["Department of Mathematics University of Illinois at Urbana\u2010Champaign  Urbana Illinois USA","\u201cSimion Stoilow\u201d Institute of Mathematics of the Romanian Academy  Bucharest Romania"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics University of Illinois at Urbana\u2010Champaign  Urbana Illinois USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"\u201cSimion Stoilow\u201d Institute of Mathematics of the Romanian Academy  Bucharest Romania","institution_ids":["https://openalex.org/I4405262991"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5071408046"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":{"value":3460,"currency":"USD","value_usd":3460},"apc_paid":null,"fwci":3.4425,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.86522527,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"298","issue":"5","first_page":"1617","last_page":"1632"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9833999872207642,"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":0.9833999872207642,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.004000000189989805,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.0013000000035390258,"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/angular-distributions","display_name":"angular distributions","score":0.5329999923706055},{"id":"https://openalex.org/keywords/gap-distribution","display_name":"gap distribution","score":0.578000009059906},{"id":"https://openalex.org/keywords/random-point-sets","display_name":"random point sets","score":0.3479999899864197},{"id":"https://openalex.org/keywords/density-function","display_name":"density function","score":0.5049999952316284}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8279807567596436},{"id":"https://openalex.org/C2780704645","wikidata":"https://www.wikidata.org/wiki/Q9251458","display_name":"Observer (physics)","level":2,"score":0.634718656539917},{"id":"https://openalex.org/C101468663","wikidata":"https://www.wikidata.org/wiki/Q1620158","display_name":"Modular design","level":2,"score":0.5925010442733765},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.5604116916656494},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.293032169342041},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09563678503036499},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/mana.12016","doi":"https://doi.org/10.1002/mana.12016","is_oa":true,"landing_page_url":"https://doi.org/10.1002/mana.12016","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/mana.12016","source":{"id":"https://openalex.org/S73458468","display_name":"Mathematische Nachrichten","issn_l":"0025-584X","issn":["0025-584X","1522-2616"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematische Nachrichten","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1002/mana.12016","doi":"https://doi.org/10.1002/mana.12016","is_oa":true,"landing_page_url":"https://doi.org/10.1002/mana.12016","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/mana.12016","source":{"id":"https://openalex.org/S73458468","display_name":"Mathematische Nachrichten","issn_l":"0025-584X","issn":["0025-584X","1522-2616"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-d","jufo-1","norway-1","poland-100","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematische Nachrichten","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4409410641.pdf","grobid_xml":"https://content.openalex.org/works/W4409410641.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1965168444","https://openalex.org/W1976003589","https://openalex.org/W2007085211","https://openalex.org/W2040783296","https://openalex.org/W2079592209","https://openalex.org/W2081163625","https://openalex.org/W2089478444","https://openalex.org/W2095898550","https://openalex.org/W2100155551","https://openalex.org/W2117353438","https://openalex.org/W2127456573","https://openalex.org/W2293973111","https://openalex.org/W2314948770","https://openalex.org/W2320336334","https://openalex.org/W2334612034","https://openalex.org/W2605819196","https://openalex.org/W2963777931","https://openalex.org/W3088705333","https://openalex.org/W3157643985","https://openalex.org/W4211076355","https://openalex.org/W4321347810","https://openalex.org/W4399851892"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"be":[2,50,115],"a":[3,53,69,75,128,145],"fixed":[4],"non\u2010zero":[5],"integer.":[6],"For":[7],"every":[8,10],"and":[9,158],"prime":[11],",":[12,42,102],"consider":[13],"the":[14,23,26,30,37,40,65,89,92,107,125,135,151,160,164],"angles":[15,100,139],"between":[16,133],"rays":[17],"from":[18,74],"an":[19],"observer":[20],"located":[21],"at":[22],"point":[24,82],"on":[25,64],"real":[27],"axis":[28],"toward":[29],"set":[31,46,59,98],"of":[32,36,47,68,78,91,99,117,127,130,137,147,166],"all":[33],"integral":[34],"solutions":[35],"equation":[38],"in":[39,71,149],"square":[41],"where":[43],".":[44,118],"This":[45,143],"points":[48,61,132],"can":[49],"seen":[51,138],"as":[52,101],"generic":[54],"model":[55],"for":[56,96,106],"any":[57,85],"target":[58],"with":[60],"randomly":[62],"distributed":[63],"integer":[66],"coordinates":[67],"square,":[70],"which,":[72],"apart":[73],"small":[76],"number":[77],"exceptions,":[79],"exactly":[80],"one":[81,155],"lies":[83],"above":[84],"abscissa.":[86],"We":[87],"prove":[88],"existence":[90,126],"limiting":[93],"gap":[94,121],"distribution":[95,122,136],"this":[97],"providing":[103],"explicit":[104],"formulas":[105],"corresponding":[108],"density":[109],"function,":[110],"which":[111,134,153],"turns":[112],"out":[113],"to":[114,156,163],"independent":[116],"The":[119],"resulted":[120],"function":[123],"shows":[124],"sequence":[129],"threshold":[131],"has":[140],"different":[141],"shapes.":[142],"provides":[144],"tool":[146],"reference":[148],"guiding":[150],"observer,":[152],"allows":[154],"find":[157],"control":[159],"position":[161],"relative":[162],"universe":[165],"observed":[167],"points.":[168]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}
