{"id":"https://openalex.org/W2964021237","doi":"https://doi.org/10.1007/s40993-016-0071-5","title":"Some mixed character sum identities of Katz II","display_name":"Some mixed character sum identities of Katz II","publication_year":2017,"publication_date":"2017-01-27","ids":{"openalex":"https://openalex.org/W2964021237","doi":"https://doi.org/10.1007/s40993-016-0071-5","mag":"2964021237"},"language":"en","primary_location":{"id":"doi:10.1007/s40993-016-0071-5","doi":"https://doi.org/10.1007/s40993-016-0071-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40993-016-0071-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40993-016-0071-5.pdf","source":{"id":"https://openalex.org/S4210215925","display_name":"Research in Number Theory","issn_l":"2363-9555","issn":["2363-9555","2522-0160"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Research in Number Theory","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s40993-016-0071-5.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032617544","display_name":"Ron Evans","orcid":"https://orcid.org/0000-0002-1184-4642","observed_orcids":["https://orcid.org/0000-0002-1184-4642"]},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ron Evans","raw_affiliation_strings":["Department of Mathematics, University of California at San Diego, La Jolla, CA, 92093-0112, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California at San Diego, La Jolla, CA, 92093-0112, USA","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110571832","display_name":"John Greene","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210115145","display_name":"University of Minnesota, Duluth","ror":"https://ror.org/01hy4qx27","country_code":"US","type":"education","lineage":["https://openalex.org/I4210115145"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"John Greene","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Minnesota-Duluth, Duluth, MN, 55812, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Minnesota-Duluth, Duluth, MN, 55812, USA","institution_ids":["https://openalex.org/I4210115145"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5032617544"],"corresponding_institution_ids":["https://openalex.org/I36258959"],"apc_list":{"value":3590,"currency":"USD","value_usd":3590},"apc_paid":{"value":3590,"currency":"USD","value_usd":3590},"fwci":0.9823,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.74755382,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":95},"biblio":{"volume":"3","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9312000274658203,"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":0.9312000274658203,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.03189999982714653,"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/T11130","display_name":"Coding theory and cryptography","score":0.008100000210106373,"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/finite-fields","display_name":"finite fields","score":0.8220000267028809},{"id":"https://openalex.org/keywords/direct-proof","display_name":"direct proof","score":0.6470000147819519}],"concepts":[{"id":"https://openalex.org/C2780861071","wikidata":"https://www.wikidata.org/wiki/Q1062934","display_name":"Character (mathematics)","level":2,"score":0.860424816608429},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.854928195476532},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7307616472244263},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5705856084823608},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5621107816696167},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.509835422039032},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.49703744053840637},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4650823473930359},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.403774619102478},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32864218950271606},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19987443089485168},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09582039713859558},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s40993-016-0071-5","doi":"https://doi.org/10.1007/s40993-016-0071-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40993-016-0071-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40993-016-0071-5.pdf","source":{"id":"https://openalex.org/S4210215925","display_name":"Research in Number Theory","issn_l":"2363-9555","issn":["2363-9555","2522-0160"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Research in Number Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1609.01429","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1609.01429","pdf_url":"https://arxiv.org/pdf/1609.01429","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.1609.01429","doi":"https://doi.org/10.48550/arxiv.1609.01429","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1609.01429","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1007/s40993-016-0071-5","doi":"https://doi.org/10.1007/s40993-016-0071-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40993-016-0071-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40993-016-0071-5.pdf","source":{"id":"https://openalex.org/S4210215925","display_name":"Research in Number Theory","issn_l":"2363-9555","issn":["2363-9555","2522-0160"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-3"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Research in Number Theory","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2964021237.pdf","grobid_xml":"https://content.openalex.org/works/W2964021237.grobid-xml"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1498968422","https://openalex.org/W1512374421","https://openalex.org/W1574883946","https://openalex.org/W1819147413","https://openalex.org/W1965468517","https://openalex.org/W1984760480","https://openalex.org/W2010958505","https://openalex.org/W2085516154","https://openalex.org/W2086269028","https://openalex.org/W2087736116","https://openalex.org/W2122278592","https://openalex.org/W2286033696","https://openalex.org/W2328215223","https://openalex.org/W2489951252","https://openalex.org/W2510585665","https://openalex.org/W4303446729"],"related_works":["https://openalex.org/W2489951252","https://openalex.org/W7114787361","https://openalex.org/W7099648921","https://openalex.org/W2111099481","https://openalex.org/W2047496983","https://openalex.org/W2112517554","https://openalex.org/W2047727389","https://openalex.org/W2125166050","https://openalex.org/W2138077421","https://openalex.org/W3153939416"],"abstract_inverted_index":{"A":[0],"conjecture":[1],"connected":[2],"with":[3],"quantum":[4],"physics":[5],"led":[6],"N.":[7],"Katz":[8],"to":[9],"discover":[10],"some":[11,100],"amazing":[12],"mixed":[13],"character":[14,103],"sum":[15,104],"identities":[16,61],"over":[17],"a":[18,26,29,46,57,74],"field":[19],"of":[20,28,59],"q":[21,24],"elements,":[22],"where":[23],"is":[25],"power":[27],"prime":[30],"$$p":[31],">3$$":[32],".":[33,85,94],"His":[34],"proof":[35,58,75],"required":[36],"deep":[37],"algebro-geometric":[38],"techniques,":[39],"and":[40,69],"he":[41],"expressed":[42],"interest":[43],"in":[44],"finding":[45],"more":[47],"straightforward":[48],"direct":[49],"proof.":[50],"The":[51],"first":[52],"author":[53],"recently":[54],"gave":[55],"such":[56,73],"his":[60],"when":[62],"$$q":[63,80],"\\equiv":[64,81],"1":[65],"\\pmod":[66,83],"4$$":[67,84],",":[68],"this":[70],"paper":[71],"provides":[72],"for":[76,90],"the":[77,96],"remaining":[78],"case":[79],"3":[82],"Our":[86],"proofs":[87],"are":[88],"valid":[89],"all":[91],"characteristics":[92],"$$p>2$$":[93],"Along":[95],"way":[97],"we":[98],"prove":[99],"elegant":[101],"new":[102],"identities.":[105]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2019-07-30T00:00:00"}
