{"id":"https://openalex.org/W2057506739","doi":"https://doi.org/10.1090/s0025-5718-01-01356-4","title":"Asymptotic properties of the spectral test, diaphony, and related quantities","display_name":"Asymptotic properties of the spectral test, diaphony, and related quantities","publication_year":2001,"publication_date":"2001-08-02","ids":{"openalex":"https://openalex.org/W2057506739","doi":"https://doi.org/10.1090/s0025-5718-01-01356-4","mag":"2057506739"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-01-01356-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01356-4","pdf_url":"https://www.ams.org/mcom/2002-71-237/S0025-5718-01-01356-4/S0025-5718-01-01356-4.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2002-71-237/S0025-5718-01-01356-4/S0025-5718-01-01356-4.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065988110","display_name":"Hannes Leeb","orcid":"https://orcid.org/0000-0002-5770-5955"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Hannes Leeb","raw_affiliation_strings":["Department of Statistics, University of Vienna, Universit\u00c3\u00a4tsstrasse 5, A-1010 Vienna, Austria","Department of Statistics, University of Vienna, Universit\u00e4tsstrasse 5, A-1010 Vienna, Austria"],"affiliations":[{"raw_affiliation_string":"Department of Statistics, University of Vienna, Universit\u00c3\u00a4tsstrasse 5, A-1010 Vienna, Austria","institution_ids":["https://openalex.org/I129774422"]},{"raw_affiliation_string":"Department of Statistics, University of Vienna, Universit\u00e4tsstrasse 5, A-1010 Vienna, Austria","institution_ids":["https://openalex.org/I129774422"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5065988110"],"corresponding_institution_ids":["https://openalex.org/I129774422"],"apc_list":null,"apc_paid":null,"fwci":0.5831,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.68521801,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"71","issue":"237","first_page":"297","last_page":"310"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T11166","display_name":"Analytic Number Theory Research","score":0.9976999759674072,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/mathematics","display_name":"Mathematics","score":0.8747199773788452},{"id":"https://openalex.org/keywords/cover","display_name":"Cover (algebra)","score":0.7132352590560913},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.672570526599884},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.6283555030822754},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5335457921028137},{"id":"https://openalex.org/keywords/spectral-power-distribution","display_name":"Spectral power distribution","score":0.5284162759780884},{"id":"https://openalex.org/keywords/spectral-function","display_name":"Spectral function","score":0.5007178783416748},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4757366180419922},{"id":"https://openalex.org/keywords/exponential-distribution","display_name":"Exponential distribution","score":0.4488235414028168},{"id":"https://openalex.org/keywords/spectral-properties","display_name":"Spectral properties","score":0.4111681282520294},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2743665874004364},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.18963465094566345}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8747199773788452},{"id":"https://openalex.org/C2780428219","wikidata":"https://www.wikidata.org/wiki/Q16952335","display_name":"Cover (algebra)","level":2,"score":0.7132352590560913},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.672570526599884},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6283555030822754},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5335457921028137},{"id":"https://openalex.org/C94360122","wikidata":"https://www.wikidata.org/wiki/Q1967557","display_name":"Spectral power distribution","level":2,"score":0.5284162759780884},{"id":"https://openalex.org/C2985105764","wikidata":"https://www.wikidata.org/wiki/Q1331626","display_name":"Spectral function","level":2,"score":0.5007178783416748},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4757366180419922},{"id":"https://openalex.org/C55350006","wikidata":"https://www.wikidata.org/wiki/Q237193","display_name":"Exponential distribution","level":2,"score":0.4488235414028168},{"id":"https://openalex.org/C2985906921","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Spectral properties","level":2,"score":0.4111681282520294},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2743665874004364},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.18963465094566345},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C147597530","wikidata":"https://www.wikidata.org/wiki/Q369472","display_name":"Computational chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-01-01356-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01356-4","pdf_url":"https://www.ams.org/mcom/2002-71-237/S0025-5718-01-01356-4/S0025-5718-01-01356-4.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-01-01356-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-01-01356-4","pdf_url":"https://www.ams.org/mcom/2002-71-237/S0025-5718-01-01356-4/S0025-5718-01-01356-4.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2057506739.pdf","grobid_xml":"https://content.openalex.org/works/W2057506739.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W13993367","https://openalex.org/W97112242","https://openalex.org/W157895250","https://openalex.org/W1533955387","https://openalex.org/W1543280314","https://openalex.org/W1553775460","https://openalex.org/W1589189986","https://openalex.org/W1604816700","https://openalex.org/W1973321757","https://openalex.org/W1983515516","https://openalex.org/W2010029425","https://openalex.org/W2023711160","https://openalex.org/W2024626809","https://openalex.org/W2031141876","https://openalex.org/W2034029624","https://openalex.org/W2040396531","https://openalex.org/W2042572314","https://openalex.org/W2088210818","https://openalex.org/W2123106057","https://openalex.org/W2951866588","https://openalex.org/W3101996984","https://openalex.org/W3105588780","https://openalex.org/W4292025355"],"related_works":["https://openalex.org/W2067732275","https://openalex.org/W2388806693","https://openalex.org/W1953762007","https://openalex.org/W2089165037","https://openalex.org/W2035503125","https://openalex.org/W4301306868","https://openalex.org/W3195628437","https://openalex.org/W3104962807","https://openalex.org/W2949225013","https://openalex.org/W1583220795"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"the":[3,19,26,29,39,49,59,64],"limit":[4],"laws":[5],"of":[6,33,38,42,67],"discrepancies":[7,41],"defined":[8],"via":[9],"exponential":[10,50],"sums,":[11],"and":[12,28,35,44,46,63],"algorithms":[13],"(with":[14],"error":[15],"bounds)":[16],"to":[17],"approximate":[18],"corresponding":[20],"distribution":[21],"functions.":[22],"The":[23],"results":[24],"cover":[25],"weighted":[27],"nonweighted":[30],"spectral":[31,60],"test":[32],"Hellekalek":[34],"various":[36],"instances":[37],"general":[40],"Hickernell":[43],"Hoogland":[45],"Kleiss":[47],"for":[48],"function":[51],"system,":[52],"as":[53,55],"well":[54],"classical":[56],"quantities":[57],"like":[58],"test,":[61],"diaphony,":[62],"Zaremba":[65],"figure":[66],"merit.":[68]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}