{"id":"https://openalex.org/W2071862846","doi":"https://doi.org/10.1155/2014/845845","title":"A Hybrid Mean Value Involving the Two-Term Exponential Sums and Two-Term Character Sums","display_name":"A Hybrid Mean Value Involving the Two-Term Exponential Sums and Two-Term Character Sums","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2071862846","doi":"https://doi.org/10.1155/2014/845845","mag":"2071862846"},"language":"en","primary_location":{"id":"doi:10.1155/2014/845845","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/845845","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/845845.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2014/845845.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028845177","display_name":"Miaohua Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I4210104252","display_name":"Air Force Engineering University","ror":"https://ror.org/00seraz22","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210104252"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liu Miaohua","raw_affiliation_strings":["Institute of Science, Air Force Engineering University, Xi\u2019an, Shaanxi 710051, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Science, Air Force Engineering University, Xi\u2019an, Shaanxi 710051, China","institution_ids":["https://openalex.org/I4210104252"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101550966","display_name":"Xiaoxue Li","orcid":"https://orcid.org/0000-0001-7939-1558"},"institutions":[{"id":"https://openalex.org/I37802460","display_name":"Northwest University","ror":"https://ror.org/00z3td547","country_code":"CN","type":"education","lineage":["https://openalex.org/I37802460"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Li Xiaoxue","raw_affiliation_strings":["Department of Mathematics, Northwest University, Xi\u2019an, Shaanxi 710127, China","Department of Mathematics, Northwest University, Xi'an, Shaanxi 710127, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Northwest University, Xi\u2019an, Shaanxi 710127, China","institution_ids":["https://openalex.org/I37802460"]},{"raw_affiliation_string":"Department of Mathematics, Northwest University, Xi'an, Shaanxi 710127, China","institution_ids":["https://openalex.org/I37802460"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101550966"],"corresponding_institution_ids":["https://openalex.org/I37802460"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.1609617,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":93},"biblio":{"volume":"2014","issue":null,"first_page":"1","last_page":"5"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":1.0,"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":1.0,"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/T11680","display_name":"Advanced Algebra and Geometry","score":0.9961000084877014,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9940999746322632,"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/term","display_name":"Term (time)","score":0.8620910048484802},{"id":"https://openalex.org/keywords/character","display_name":"Character (mathematics)","score":0.8526192903518677},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7846605777740479},{"id":"https://openalex.org/keywords/gauss-sum","display_name":"Gauss sum","score":0.7007634043693542},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.695699155330658},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.6249388456344604},{"id":"https://openalex.org/keywords/asymptotic-formula","display_name":"Asymptotic formula","score":0.5883683562278748},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4941404163837433},{"id":"https://openalex.org/keywords/mean-value","display_name":"Mean value","score":0.4335300922393799},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.30539846420288086},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2714881896972656},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2542129158973694},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20365989208221436}],"concepts":[{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.8620910048484802},{"id":"https://openalex.org/C2780861071","wikidata":"https://www.wikidata.org/wiki/Q1062934","display_name":"Character (mathematics)","level":2,"score":0.8526192903518677},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7846605777740479},{"id":"https://openalex.org/C186348414","wikidata":"https://www.wikidata.org/wiki/Q526221","display_name":"Gauss sum","level":2,"score":0.7007634043693542},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.695699155330658},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.6249388456344604},{"id":"https://openalex.org/C24209939","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic formula","level":2,"score":0.5883683562278748},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4941404163837433},{"id":"https://openalex.org/C2988626262","wikidata":"https://www.wikidata.org/wiki/Q2796622","display_name":"Mean value","level":2,"score":0.4335300922393799},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.30539846420288086},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2714881896972656},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2542129158973694},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20365989208221436},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2014/845845","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/845845","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/845845.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1425305562","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1425305562","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"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":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:845845","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2014/845845.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:7e6e0196824f452eb7e6d96764fc72ad","is_oa":true,"landing_page_url":"https://doaj.org/article/7e6e0196824f452eb7e6d96764fc72ad","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2014 (2014)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2014/845845","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/845845","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/845845.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.41999998688697815,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G1764318812","display_name":null,"funder_award_id":"11371291","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2458985097","display_name":null,"funder_award_id":"11371291","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2071862846.pdf","grobid_xml":"https://content.openalex.org/works/W2071862846.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1495550473","https://openalex.org/W1995465778","https://openalex.org/W2044299069","https://openalex.org/W2047727389","https://openalex.org/W2098883364","https://openalex.org/W2100522424","https://openalex.org/W2104428487","https://openalex.org/W2112517554","https://openalex.org/W2274813658","https://openalex.org/W2696583186"],"related_works":["https://openalex.org/W2997791543","https://openalex.org/W2876959735","https://openalex.org/W1968822906","https://openalex.org/W2351051352","https://openalex.org/W2468561932","https://openalex.org/W2029735262","https://openalex.org/W4387098538","https://openalex.org/W2030128827","https://openalex.org/W2085934387","https://openalex.org/W2127471060"],"abstract_inverted_index":{"The":[0],"main":[1],"purpose":[2],"of":[3,10],"this":[4],"paper":[5],"is":[6],"using":[7],"the":[8,14,21,27],"properties":[9],"Gauss":[11],"sums":[12,18,30,34],"and":[13,31,35],"estimate":[15],"for":[16,41],"character":[17,33],"to":[19],"study":[20],"hybrid":[22],"mean":[23],"value":[24],"problem":[25],"involving":[26],"two-term":[28,32],"exponential":[29],"give":[36],"an":[37],"interesting":[38],"asymptotic":[39],"formula":[40],"it.":[42]},"counts_by_year":[{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}