{"id":"https://openalex.org/W3202952117","doi":"https://doi.org/10.1142/s1793830921501524","title":"Deep learning-based approximation of Goldbach partition function","display_name":"Deep learning-based approximation of Goldbach partition function","publication_year":2021,"publication_date":"2021-07-10","ids":{"openalex":"https://openalex.org/W3202952117","doi":"https://doi.org/10.1142/s1793830921501524","mag":"3202952117"},"language":"en","primary_location":{"id":"doi:10.1142/s1793830921501524","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830921501524","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","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/A5100319878","display_name":"Eunmi Kim","orcid":"https://orcid.org/0000-0001-8209-0190"},"institutions":[{"id":"https://openalex.org/I138925566","display_name":"Ewha Womans University","ror":"https://ror.org/053fp5c05","country_code":"KR","type":"education","lineage":["https://openalex.org/I138925566"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Eunmi Kim","raw_affiliation_strings":["Institute of Mathematical Sciences, Ewha Womans University, 52 Ewhayeodae-gil, Seodaemun-gu, Seoul 03760, Republic of Korea"],"raw_orcid":"https://orcid.org/0000-0001-8209-0190","affiliations":[{"raw_affiliation_string":"Institute of Mathematical Sciences, Ewha Womans University, 52 Ewhayeodae-gil, Seodaemun-gu, Seoul 03760, Republic of Korea","institution_ids":["https://openalex.org/I138925566"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5100319878"],"corresponding_institution_ids":["https://openalex.org/I138925566"],"apc_list":null,"apc_paid":null,"fwci":0.6297,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.66339214,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"14","issue":"05","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":0.9998999834060669,"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":0.9998999834060669,"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":0.9994000196456909,"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/T11567","display_name":"semigroups and automata theory","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/goldbachs-conjecture","display_name":"Goldbach's conjecture","score":0.9506525993347168},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.7330173850059509},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.5873096585273743},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5453807711601257},{"id":"https://openalex.org/keywords/partition-function","display_name":"Partition function (quantum field theory)","score":0.5401337146759033},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4820757508277893},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4699692130088806},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.45390617847442627},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.324131578207016},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1369118094444275},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.05510878562927246}],"concepts":[{"id":"https://openalex.org/C143732363","wikidata":"https://www.wikidata.org/wiki/Q485520","display_name":"Goldbach's conjecture","level":3,"score":0.9506525993347168},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.7330173850059509},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5873096585273743},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5453807711601257},{"id":"https://openalex.org/C2778401447","wikidata":"https://www.wikidata.org/wiki/Q7140637","display_name":"Partition function (quantum field theory)","level":2,"score":0.5401337146759033},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4820757508277893},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4699692130088806},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.45390617847442627},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.324131578207016},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1369118094444275},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.05510878562927246},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793830921501524","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793830921501524","pdf_url":null,"source":{"id":"https://openalex.org/S178434951","display_name":"Discrete Mathematics Algorithms and Applications","issn_l":"1793-8309","issn":["1793-8309","1793-8317"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics, Algorithms and Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3691648678","display_name":null,"funder_award_id":"2020R1I1A1A01065877","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"},{"id":"https://openalex.org/G4484748457","display_name":null,"funder_award_id":"2019R1A6A1A11051177","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"}],"funders":[{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1965564252","https://openalex.org/W2034249254","https://openalex.org/W2071743058","https://openalex.org/W2390833879","https://openalex.org/W2963141769"],"related_works":["https://openalex.org/W3195011978","https://openalex.org/W4206715184","https://openalex.org/W4231989170","https://openalex.org/W4328052772","https://openalex.org/W2488656357","https://openalex.org/W6389680","https://openalex.org/W1497177890","https://openalex.org/W2737272503","https://openalex.org/W4294567731","https://openalex.org/W2808407214"],"abstract_inverted_index":{"Goldbach\u2019s":[0],"conjecture":[1],"is":[2],"one":[3],"of":[4,23,32,34,45,51],"the":[5,24,30],"oldest":[6],"and":[7,59],"famous":[8],"unproved":[9],"problems":[10],"in":[11],"number":[12,31,38,52],"theory.":[13],"Using":[14],"a":[15,43,61],"deep":[16],"learning":[17],"model,":[18],"we":[19],"obtain":[20],"an":[21,36],"approximation":[22],"Goldbach":[25],"partition":[26],"function,":[27],"which":[28,65],"counts":[29],"ways":[33],"representing":[35],"even":[37],"greater":[39],"than":[40],"4":[41],"as":[42,57],"sum":[44],"two":[46],"primes.":[47],"We":[48],"use":[49],"residues":[50],"modulo":[53],"first":[54],"25":[55],"primes":[56],"features":[58],"archive":[60],"more":[62],"accurate":[63],"approximation,":[64],"reduces":[66],"error":[67],"rate":[68],"from":[69],"[Formula:":[70,74],"see":[71,75],"text]":[72],"to":[73],"text].":[76]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
