{"id":"https://openalex.org/W2088352100","doi":"https://doi.org/10.1017/s0963548302005436","title":"Some Constructions in the Inverse Spectral Theory of Cyclic Groups","display_name":"Some Constructions in the Inverse Spectral Theory of Cyclic Groups","publication_year":2003,"publication_date":"2003-03-01","ids":{"openalex":"https://openalex.org/W2088352100","doi":"https://doi.org/10.1017/s0963548302005436","mag":"2088352100"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548302005436","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548302005436","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","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/A5100610718","display_name":"Ben Green","orcid":"https://orcid.org/0000-0002-2224-1193"},"institutions":[{"id":"https://openalex.org/I204442077","display_name":"Trinity College","ror":"https://ror.org/019dhar59","country_code":"CA","type":"education","lineage":["https://openalex.org/I204442077"]},{"id":"https://openalex.org/I241749","display_name":"University of Cambridge","ror":"https://ror.org/013meh722","country_code":"GB","type":"education","lineage":["https://openalex.org/I241749"]}],"countries":["CA","GB"],"is_corresponding":true,"raw_author_name":"BEN GREEN","raw_affiliation_strings":["Trinity College, Cambridge CB2 1TQ, England (e-mail: Ben Green","Trinity College, Cambridge CB2 1TQ, England (e-mail: Ben Green bjg23@hermes.cam.ac.uk)#TAB#"],"affiliations":[{"raw_affiliation_string":"Trinity College, Cambridge CB2 1TQ, England (e-mail: Ben Green","institution_ids":["https://openalex.org/I204442077"]},{"raw_affiliation_string":"Trinity College, Cambridge CB2 1TQ, England (e-mail: Ben Green bjg23@hermes.cam.ac.uk)#TAB#","institution_ids":["https://openalex.org/I241749"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100610718"],"corresponding_institution_ids":["https://openalex.org/I204442077","https://openalex.org/I241749"],"apc_list":null,"apc_paid":null,"fwci":2.2055,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.85879397,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"12","issue":"2","first_page":"127","last_page":"138"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9993000030517578,"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"}},"topics":[{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9993000030517578,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9679999947547913,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9465000033378601,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/parsevals-theorem","display_name":"Parseval's theorem","score":0.8262595534324646},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8046589493751526},{"id":"https://openalex.org/keywords/spectrum","display_name":"Spectrum (functional analysis)","score":0.6056495904922485},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5842572450637817},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.58265221118927},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.483847051858902},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4821740984916687},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.46803075075149536},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3845561444759369},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37056055665016174},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.27857697010040283},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23480546474456787},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10096350312232971},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09775590896606445},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.06877076625823975},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06363660097122192}],"concepts":[{"id":"https://openalex.org/C89451469","wikidata":"https://www.wikidata.org/wiki/Q1443036","display_name":"Parseval's theorem","level":5,"score":0.8262595534324646},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8046589493751526},{"id":"https://openalex.org/C156778621","wikidata":"https://www.wikidata.org/wiki/Q1365748","display_name":"Spectrum (functional analysis)","level":2,"score":0.6056495904922485},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5842572450637817},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.58265221118927},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.483847051858902},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4821740984916687},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.46803075075149536},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3845561444759369},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37056055665016174},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.27857697010040283},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23480546474456787},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10096350312232971},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09775590896606445},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.06877076625823975},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06363660097122192},{"id":"https://openalex.org/C76563020","wikidata":"https://www.wikidata.org/wiki/Q4817582","display_name":"Fractional Fourier transform","level":4,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1017/s0963548302005436","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548302005436","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/ed94ea0a-b472-4ac1-9974-9e836c60c84c","is_oa":false,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/ed94ea0a-b472-4ac1-9974-9e836c60c84c","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Green, BJ 2003, 'Some constructions in the inverse spectral theory of cyclic groups', COmbinatorics Probability & Computing, vol. 12 (2), pp. 127 - 138.","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1262279904","https://openalex.org/W1837752427","https://openalex.org/W1970446299","https://openalex.org/W1991135809","https://openalex.org/W2088402854","https://openalex.org/W2144037778"],"related_works":["https://openalex.org/W2495194047","https://openalex.org/W1522297789","https://openalex.org/W2164846160","https://openalex.org/W1983104818","https://openalex.org/W2391387784","https://openalex.org/W2951524812","https://openalex.org/W4298118036","https://openalex.org/W4296137464","https://openalex.org/W2179977742","https://openalex.org/W1872476839"],"abstract_inverted_index":{"The":[0],"results":[1],"of":[2,9,17,26,33,48,53,67,87,121],"this":[3],"paper":[4],"concern":[5],"the":[6,15,23,51,54,85],"'large":[7],"spectra'":[8],"sets,":[10],"by":[11],"which":[12,22,91],"we":[13],"mean":[14],"set":[16,86],"points":[18,88],"in":[19,69],"F-p(x)":[20],"at":[21],"Fourier":[24],"transform":[25],"a":[27,45,65,118],"characteristic":[28],"function":[29],"chi(A),":[30],"A":[31],"subset":[32],"or":[34,98],"equal":[35,99],"to":[36,100],"F-p,":[37],"P":[38],"can":[39,105],"be":[40,106],"large.":[41],"We":[42,73],"show":[43,75],"that":[44,76,112],"recent":[46],"result":[47,61],"Chang":[49],"concerning":[50],"structure":[52],"large":[55],"spectrum":[56],"is":[57,84],"best":[58],"possible.":[59],"Chang's":[60],"has":[62],"already":[63],"found":[64],"number":[66,71],"applications":[68],"combinatorial":[70],"theory.":[72],"also":[74],"if":[77,82],"\\A\\":[78],"=":[79],"[p/2],":[80],"and":[81],"R":[83,109],"r":[89],"for":[90],"\\(\u03c7)":[92],"over":[93],"cap":[94],"(A)(r)\\":[95],"greater":[96],"than":[97,111,116],"alphap,":[101],"then":[102],"almost":[103],"nothing":[104],"said":[107],"about":[108],"other":[110],"\\R\\":[113],"much":[114],"less":[115],"alpha(-2),":[117],"trivial":[119],"consequence":[120],"Parseval's":[122],"theorem.":[123]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}