{"id":"https://openalex.org/W2029229255","doi":"https://doi.org/10.1080/10586458.1992.10504252","title":"Fast Fourier Analysis for SL<sub>2</sub>over a Finite Field and Related Numerical Experiments","display_name":"Fast Fourier Analysis for SL<sub>2</sub>over a Finite Field and Related Numerical Experiments","publication_year":1992,"publication_date":"1992-01-01","ids":{"openalex":"https://openalex.org/W2029229255","doi":"https://doi.org/10.1080/10586458.1992.10504252","mag":"2029229255"},"language":"en","primary_location":{"id":"doi:10.1080/10586458.1992.10504252","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.1992.10504252","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060219657","display_name":"John Lafferty","orcid":"https://orcid.org/0000-0002-5929-220X"},"institutions":[{"id":"https://openalex.org/I4210114115","display_name":"IBM Research - Thomas J. Watson Research Center","ror":"https://ror.org/0265w5591","country_code":"US","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210114115"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"John D. Lafferty","raw_affiliation_strings":["IBM Research Division. Thomas .I. Watson Research Center , Yorktown Heights , NY , 10598 E-mail: jlaff@watson.ibm.com"],"affiliations":[{"raw_affiliation_string":"IBM Research Division. Thomas .I. Watson Research Center , Yorktown Heights , NY , 10598 E-mail: jlaff@watson.ibm.com","institution_ids":["https://openalex.org/I4210114115"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072455364","display_name":"Daniel N. Rockmore","orcid":"https://orcid.org/0000-0001-5411-9224"},"institutions":[{"id":"https://openalex.org/I107672454","display_name":"Dartmouth College","ror":"https://ror.org/049s0rh22","country_code":"US","type":"education","lineage":["https://openalex.org/I107672454"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel Rockmore","raw_affiliation_strings":["Department of Mathematics , Columbia University , New York , NY , 10027 ; Department of Mathematics , Dartmouth College , Hanover , NH , 03755 E-mail: rockmore@aruba.dart.mOuth.edu"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , Columbia University , New York , NY , 10027 ; Department of Mathematics , Dartmouth College , Hanover , NH , 03755 E-mail: rockmore@aruba.dart.mOuth.edu","institution_ids":["https://openalex.org/I107672454"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5060219657"],"corresponding_institution_ids":["https://openalex.org/I4210114115"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":39,"citation_normalized_percentile":{"value":0.17742947,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"1","issue":"2","first_page":"115","last_page":"139"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10849","display_name":"Finite Group Theory Research","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7593176364898682},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.7352734804153442},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.584522008895874},{"id":"https://openalex.org/keywords/cayley-graph","display_name":"Cayley graph","score":0.5720701217651367},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4876236021518707},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.48447084426879883},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.46199989318847656},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.42775946855545044},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3703470230102539},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2753176689147949},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22094249725341797}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7593176364898682},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.7352734804153442},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.584522008895874},{"id":"https://openalex.org/C120204988","wikidata":"https://www.wikidata.org/wiki/Q859174","display_name":"Cayley graph","level":3,"score":0.5720701217651367},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4876236021518707},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.48447084426879883},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.46199989318847656},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42775946855545044},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3703470230102539},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2753176689147949},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22094249725341797},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10586458.1992.10504252","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10586458.1992.10504252","pdf_url":null,"source":{"id":"https://openalex.org/S119636414","display_name":"Experimental Mathematics","issn_l":"1058-6458","issn":["1058-6458","1944-950X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Experimental Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W195788117","https://openalex.org/W382810004","https://openalex.org/W594938858","https://openalex.org/W1489939486","https://openalex.org/W1515707356","https://openalex.org/W1534739489","https://openalex.org/W1560594658","https://openalex.org/W1596185498","https://openalex.org/W1596709027","https://openalex.org/W1631603072","https://openalex.org/W1677255974","https://openalex.org/W1971407031","https://openalex.org/W1978423589","https://openalex.org/W1986263670","https://openalex.org/W1993111701","https://openalex.org/W1999911623","https://openalex.org/W2018483531","https://openalex.org/W2019435258","https://openalex.org/W2024016477","https://openalex.org/W2026391697","https://openalex.org/W2040077566","https://openalex.org/W2049622697","https://openalex.org/W2054624527","https://openalex.org/W2092852220","https://openalex.org/W2093674973","https://openalex.org/W2151436648","https://openalex.org/W2166435158","https://openalex.org/W2179504188","https://openalex.org/W2324705588","https://openalex.org/W2327895136","https://openalex.org/W2328799190","https://openalex.org/W2502697445","https://openalex.org/W4211241601","https://openalex.org/W4252681893"],"related_works":["https://openalex.org/W2074270182","https://openalex.org/W2005469817","https://openalex.org/W999425096","https://openalex.org/W4297665610","https://openalex.org/W4287724448","https://openalex.org/W2141072651","https://openalex.org/W1535963902","https://openalex.org/W2002689282","https://openalex.org/W2027653655","https://openalex.org/W2964090935"],"abstract_inverted_index":{"We":[0,166],"study":[1],"the":[2,9,18,73,81,84,103,106,110,150,160,168],"complexity":[3,82],"of":[4,21,26,30,83,100,123,130,149,159,162],"performing":[5,50],"Fourier":[6,31,51,87],"analysis":[7],"for":[8,33,49,57],"group":[10],"SL2(F":[11],"q":[12,16,22,39,42,136],"),":[13],"where":[14,72],"F":[15],"is":[17,76,142],"finite":[19],"field":[20],"elements.":[23],"Direct":[24],"computation":[25],"a":[27,34],"complete":[28],"set":[29],"transforms":[32],"complex-valued":[35],"function":[36],"f":[37],"onSL2(F":[38],")":[40,137],"requires":[41],"6":[43],"operations.":[44],"A":[45],"similar":[46],"bound":[47,63],"holds":[48],"inversion.":[52],"Here":[53],"we":[54,91],"show":[55],"that":[56,127],"both":[58],"operations":[59],"this":[60],"naive":[61],"upper":[62],"may":[64],"be":[65],"reduced":[66],"to":[67,108],"O(q":[68],"4":[69],"log":[70],"q),":[71],"implied":[74],"constant":[75],"universal,":[77],"depending":[78],"only":[79],"on":[80,95,133],"\u201cclassical\u201d":[85],"fast":[86],"transform.":[88],"The":[89],"techniques":[90],"use":[92],"depend":[93],"strongly":[94],"explicit":[96],"construct":[97,109],"io":[98],"ns":[99],"matrix":[101,111],"representationsof":[102],"group.":[104],"Additionally,":[105],"ability":[107],"representations":[112],"permits":[113,155],"certain":[114,128],"numerical":[115,157],"experiments.":[116],"By":[117],"quite":[118],"general":[119],"methods,":[120],"recent":[121],"work":[122],"others":[124],"has":[125],"shown":[126],"families":[129],"Cayley":[131,164],"graphs":[132],"SL2":[134],"(F":[135],"are":[138],"expanders.":[139],"However,":[140],"little":[141],"known":[143],"about":[144],"their":[145],"exact":[146],"spectra.":[147],"Computation":[148],"relevant":[151],"Four":[152],"ier":[153],"transform":[154],"extensive":[156],"investigations":[158],"spectra":[161],"these":[163],"graphs.":[165],"explain":[167],"associated":[169],"calculation":[170],"and":[171],"include":[172],"illustrative":[173],"figures.":[174]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
