{"id":"https://openalex.org/W4409956581","doi":"https://doi.org/10.1155/ijmm/8863564","title":"Lower Bound for the Class Number of Q49m2+4m","display_name":"Lower Bound for the Class Number of Q49m2+4m","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4409956581","doi":"https://doi.org/10.1155/ijmm/8863564"},"language":"en","primary_location":{"id":"doi:10.1155/ijmm/8863564","is_oa":true,"landing_page_url":"https://doi.org/10.1155/ijmm/8863564","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/ijmm/8863564","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/ijmm/8863564","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5117383611","display_name":"Rahaf Jihny","orcid":null},"institutions":[{"id":"https://openalex.org/I4210100496","display_name":"Al Andalus University","ror":"https://ror.org/00hdydj55","country_code":"SY","type":"education","lineage":["https://openalex.org/I4210100496"]},{"id":"https://openalex.org/I56085075","display_name":"University of Tartu","ror":"https://ror.org/03z77qz90","country_code":"EE","type":"education","lineage":["https://openalex.org/I56085075"]}],"countries":["EE","SY"],"is_corresponding":false,"raw_author_name":"Rahaf Jihny","raw_affiliation_strings":["Department of Mathematics ,  Faculty of Science ,  Tartous University ,  Tartous ,  Syria ,  tartous-univ.edu.sy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics ,  Faculty of Science ,  Tartous University ,  Tartous ,  Syria ,  tartous-univ.edu.sy","institution_ids":["https://openalex.org/I56085075","https://openalex.org/I4210100496"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067320460","display_name":"Boushra Darrag","orcid":"https://orcid.org/0000-0002-5005-7537"},"institutions":[{"id":"https://openalex.org/I4210100496","display_name":"Al Andalus University","ror":"https://ror.org/00hdydj55","country_code":"SY","type":"education","lineage":["https://openalex.org/I4210100496"]},{"id":"https://openalex.org/I56085075","display_name":"University of Tartu","ror":"https://ror.org/03z77qz90","country_code":"EE","type":"education","lineage":["https://openalex.org/I56085075"]}],"countries":["EE","SY"],"is_corresponding":false,"raw_author_name":"Boushra Darrag","raw_affiliation_strings":["Department of Mathematics ,  Faculty of Science ,  Tartous University ,  Tartous ,  Syria ,  tartous-univ.edu.sy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics ,  Faculty of Science ,  Tartous University ,  Tartous ,  Syria ,  tartous-univ.edu.sy","institution_ids":["https://openalex.org/I56085075","https://openalex.org/I4210100496"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011015958","display_name":"Ahmad Issa","orcid":"https://orcid.org/0000-0003-4768-0034"},"institutions":[{"id":"https://openalex.org/I4210100496","display_name":"Al Andalus University","ror":"https://ror.org/00hdydj55","country_code":"SY","type":"education","lineage":["https://openalex.org/I4210100496"]},{"id":"https://openalex.org/I56085075","display_name":"University of Tartu","ror":"https://ror.org/03z77qz90","country_code":"EE","type":"education","lineage":["https://openalex.org/I56085075"]}],"countries":["EE","SY"],"is_corresponding":true,"raw_author_name":"Ahmad Issa","raw_affiliation_strings":["Department of Mathematics ,  Faculty of Science ,  Tartous University ,  Tartous ,  Syria ,  tartous-univ.edu.sy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics ,  Faculty of Science ,  Tartous University ,  Tartous ,  Syria ,  tartous-univ.edu.sy","institution_ids":["https://openalex.org/I56085075","https://openalex.org/I4210100496"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5011015958"],"corresponding_institution_ids":["https://openalex.org/I4210100496","https://openalex.org/I56085075"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":2.4014,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.8900495,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"2025","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9477999806404114,"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":0.9477999806404114,"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/mathematics","display_name":"Mathematics","score":0.8938320875167847},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6185508966445923},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5022377967834473},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4566231966018677},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3399515151977539},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18346574902534485}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8938320875167847},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6185508966445923},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5022377967834473},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4566231966018677},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3399515151977539},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18346574902534485},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/ijmm/8863564","is_oa":true,"landing_page_url":"https://doi.org/10.1155/ijmm/8863564","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/ijmm/8863564","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jijmms:8863564","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/ijmms/2025/8863564.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:ae1e634d9aea499094c9208e6415f79c","is_oa":true,"landing_page_url":"https://doaj.org/article/ae1e634d9aea499094c9208e6415f79c","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Mathematics and Mathematical Sciences, Vol 2025 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/ijmm/8863564","is_oa":true,"landing_page_url":"https://doi.org/10.1155/ijmm/8863564","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/ijmm/8863564","source":{"id":"https://openalex.org/S151851439","display_name":"International Journal of Mathematics and Mathematical Sciences","issn_l":"0161-1712","issn":["0161-1712","1687-0425"],"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":"International Journal of Mathematics and Mathematical Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4409956581.pdf","grobid_xml":"https://content.openalex.org/works/W4409956581.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W106636584","https://openalex.org/W1519054461","https://openalex.org/W1977687211","https://openalex.org/W2043883213","https://openalex.org/W2063716569","https://openalex.org/W3003294621","https://openalex.org/W3029740201","https://openalex.org/W3134074660","https://openalex.org/W4210376439","https://openalex.org/W4252357022","https://openalex.org/W4318541650","https://openalex.org/W6911280284"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"obtain":[4],"an":[5,39],"explicit":[6],"lower":[7],"bound":[8],"for":[9,53],"the":[10,57],"class":[11],"number":[12],"of":[13,50,56],"real":[14,59],"quadratic":[15,60],"field":[16],",":[17],"where":[18],"D":[19],"=":[20],"49":[21],"m":[22,26,33],"2":[23,35],"+":[24],"4":[25],"is":[27],"a":[28],"square\u2010free":[29],"positive":[30,41],"integer":[31],"and":[32],"\u2261":[34],"(mod":[36],"7)":[37],"be":[38],"odd":[40],"integer.":[42],"The":[43],"main":[44],"tools":[45],"used":[46],"are":[47],"special":[48],"values":[49],"zeta":[51],"functions":[52],"ideal":[54],"classes":[55],"respective":[58],"fields.":[61]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
