{"id":"https://openalex.org/W2118927928","doi":"https://doi.org/10.1109/tit.2009.2023720","title":"On Certain Values of Kloosterman Sums","display_name":"On Certain Values of Kloosterman Sums","publication_year":2009,"publication_date":"2009-07-18","ids":{"openalex":"https://openalex.org/W2118927928","doi":"https://doi.org/10.1109/tit.2009.2023720","mag":"2118927928"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2009.2023720","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2009.2023720","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","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/A5091179781","display_name":"Marko Moisio","orcid":null},"institutions":[{"id":"https://openalex.org/I79765343","display_name":"University of Vaasa","ror":"https://ror.org/03769b225","country_code":"FI","type":"education","lineage":["https://openalex.org/I79765343"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Marko J. Moisio","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Vaasa, Vaasa, Finland","Dept. of Math. & Stat., Univ. of Vaasa, Vaasa, Finland"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Vaasa, Vaasa, Finland","institution_ids":["https://openalex.org/I79765343"]},{"raw_affiliation_string":"Dept. of Math. & Stat., Univ. of Vaasa, Vaasa, Finland","institution_ids":["https://openalex.org/I79765343"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5091179781"],"corresponding_institution_ids":["https://openalex.org/I79765343"],"apc_list":null,"apc_paid":null,"fwci":2.1809,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.89378458,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"55","issue":"8","first_page":"3563","last_page":"3564"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994000196456909,"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"}},{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9987999796867371,"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/T11166","display_name":"Analytic Number Theory Research","score":0.9855999946594238,"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/conjecture","display_name":"Conjecture","score":0.5457680225372314},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.19880729913711548},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.19306135177612305}],"concepts":[{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5457680225372314},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.19880729913711548},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.19306135177612305}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2009.2023720","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2009.2023720","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.244.2234","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.244.2234","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0903.4419v2.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.244.5270","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.244.5270","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/0903.4419v3.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1479708694","https://openalex.org/W1585566083","https://openalex.org/W1592261758","https://openalex.org/W2079239522","https://openalex.org/W2095108458","https://openalex.org/W2098933212","https://openalex.org/W2124745295","https://openalex.org/W2163557578","https://openalex.org/W2613956024"],"related_works":["https://openalex.org/W3194471551","https://openalex.org/W4375956809","https://openalex.org/W1581373162","https://openalex.org/W2039864950","https://openalex.org/W4288279572","https://openalex.org/W2784911598","https://openalex.org/W4297950433","https://openalex.org/W4300899577","https://openalex.org/W4287023968","https://openalex.org/W1973978937"],"abstract_inverted_index":{"Let":[0],"<i":[1,11,23,34,48,58,65,76,86],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[2,5,8,12,24,27,30,35,49,59,62,66,69,72,77,80,83,87],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">K</i>":[3,78],"<sub":[4,26,61,68,79],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">q</sub>":[6,28,63,70,81],"<sup":[7,29,71,82],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sup>":[9,31,73,84],"(":[10,85],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">a</i>":[13,50,88],")":[14,89],"be":[15,134],"a":[16,123],"Kloosterman":[17],"sum":[18],"over":[19],"the":[20,55,97,118,121],"finite":[21],"field":[22],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">F</i>":[25,60,67],"of":[32,64,120,126,128],"characteristic":[33],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">p</i>":[36],".":[37],"In":[38],"this":[39],"note":[40],"so":[41],"called":[42],"subfield":[43,57,98],"conjecture":[44,99],"is":[45,108],"proved:":[46],"if":[47],"ne":[51,90],"0":[52],"belongs":[53],"to":[54,113,133],"proper":[56],",":[74],"then":[75],"-1.":[91],"This":[92],"completes":[93],"recent":[94],"works":[95],"on":[96],"by":[100,110],"Shparlinski,":[101],"and":[102,104],"Moisio":[103],"Lisonek.":[105],"The":[106],"problem":[107],"motivated":[109],"some":[111],"applications":[112],"bent":[114],"functions.":[115],"Moreover,":[116],"in":[117],"course":[119],"proof":[122],"large":[124],"class":[125],"translates":[127],"Dickson":[129],"polynomials":[130],"are":[131],"shown":[132],"irreducible.":[135]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
