Pub Date : 2023-01-30DOI: 10.1007/s11139-023-00698-1
Dongho Byeon
{"title":"Real quadratic fields with odd class number divisible by 3","authors":"Dongho Byeon","doi":"10.1007/s11139-023-00698-1","DOIUrl":"https://doi.org/10.1007/s11139-023-00698-1","url":null,"abstract":"","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"62 1","pages":"755 - 759"},"PeriodicalIF":0.7,"publicationDate":"2023-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42614305","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the class number one problem for real quadratic fields $mathbb{Q}(sqrt{9m^2+ 4m})$, where $m$ is an odd integer. We show that for $m equiv 1 pmod 3$ there is only one such field with class number one and only one such field with class number two.
{"title":"Fields of small class number in the family $$mathbb {Q}(sqrt{9m^2+4m})$$","authors":"Nimish Kumar Mahapatra, Prem Prakash Pandey, Mahesh Kumar Ram","doi":"10.1007/s11139-022-00695-w","DOIUrl":"https://doi.org/10.1007/s11139-022-00695-w","url":null,"abstract":"We study the class number one problem for real quadratic fields $mathbb{Q}(sqrt{9m^2+ 4m})$, where $m$ is an odd integer. We show that for $m equiv 1 pmod 3$ there is only one such field with class number one and only one such field with class number two.","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135440715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-30DOI: 10.1007/s11139-022-00696-9
WU-XIA Ma, Xingfeng Jiang
{"title":"On the largest sizes of $$(s,qspm 1)$$-core partitions with parts of the same parity","authors":"WU-XIA Ma, Xingfeng Jiang","doi":"10.1007/s11139-022-00696-9","DOIUrl":"https://doi.org/10.1007/s11139-022-00696-9","url":null,"abstract":"","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49629638","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-27DOI: 10.1007/s11139-022-00645-6
Ying Zhang, Wenlong Zhang, Jingjing Zhang
{"title":"Several q-series transformation formulas and new Hecke–Rogers type series identities","authors":"Ying Zhang, Wenlong Zhang, Jingjing Zhang","doi":"10.1007/s11139-022-00645-6","DOIUrl":"https://doi.org/10.1007/s11139-022-00645-6","url":null,"abstract":"","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"60 1","pages":"627-657"},"PeriodicalIF":0.7,"publicationDate":"2023-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46652063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-24DOI: 10.1007/s11139-022-00691-0
D. Marques, P. Trojovský
{"title":"On the size of roots of a family of polynomials related to linear recurrence sequences","authors":"D. Marques, P. Trojovský","doi":"10.1007/s11139-022-00691-0","DOIUrl":"https://doi.org/10.1007/s11139-022-00691-0","url":null,"abstract":"","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"61 1","pages":"851 - 871"},"PeriodicalIF":0.7,"publicationDate":"2023-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48900102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-24DOI: 10.1007/s11139-022-00631-y
Liqun Hu
{"title":"Two results on unlike powers of primes and powers of 2 in the Waring–Goldbach problem","authors":"Liqun Hu","doi":"10.1007/s11139-022-00631-y","DOIUrl":"https://doi.org/10.1007/s11139-022-00631-y","url":null,"abstract":"","PeriodicalId":54511,"journal":{"name":"Ramanujan Journal","volume":"60 1","pages":"1081-1094"},"PeriodicalIF":0.7,"publicationDate":"2023-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46250049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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