{"title":"Linear independence of odd periods of modular forms","authors":"Austin Lei, Tianyu Ni, Hui Xue","doi":"10.1007/s40993-023-00439-9","DOIUrl":"https://doi.org/10.1007/s40993-023-00439-9","url":null,"abstract":"","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"1 1","pages":"1-20"},"PeriodicalIF":0.8,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82166958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A note on badly approximable systems of linear forms over a field of formal series","authors":"Mumtaz Hussain, N. Shulga","doi":"10.1007/s40993-023-00437-x","DOIUrl":"https://doi.org/10.1007/s40993-023-00437-x","url":null,"abstract":"","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"27 1","pages":"1-13"},"PeriodicalIF":0.8,"publicationDate":"2023-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81483668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the Iwasawa invariants of prime cyclotomic fields","authors":"Sey Y. Kim","doi":"10.1007/s40993-023-00435-z","DOIUrl":"https://doi.org/10.1007/s40993-023-00435-z","url":null,"abstract":"","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"15 1","pages":"1-20"},"PeriodicalIF":0.8,"publicationDate":"2023-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79099814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the adjoint of higher order Serre derivatives","authors":"M. Charan","doi":"10.1007/s40993-023-00438-w","DOIUrl":"https://doi.org/10.1007/s40993-023-00438-w","url":null,"abstract":"","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"15 1","pages":"1-8"},"PeriodicalIF":0.8,"publicationDate":"2023-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85021942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Identities associated to a generalized divisor function and modified Bessel function","authors":"D. Banerjee, B. Maji","doi":"10.1007/s40993-023-00431-3","DOIUrl":"https://doi.org/10.1007/s40993-023-00431-3","url":null,"abstract":"","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"15 1","pages":"1-29"},"PeriodicalIF":0.8,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89071851","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Modular forms on $${{,textrm{SU},}}(2,1)$$ with weight $$frac{1}{3}$$","authors":"E. Freitag, Richard M. Hill","doi":"10.1007/s40993-022-00361-6","DOIUrl":"https://doi.org/10.1007/s40993-022-00361-6","url":null,"abstract":"","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"38 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87504722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The probability of non-isomorphic group structures of isogenous elliptic curves in finite field extensions, I","authors":"J. Cullinan, N. Kaplan","doi":"10.1007/s40993-023-00456-8","DOIUrl":"https://doi.org/10.1007/s40993-023-00456-8","url":null,"abstract":"","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"57 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2023-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72830781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Unlikely intersections on the <i>p</i>-adic formal ball.","authors":"Vlad Serban","doi":"10.1007/s40993-023-00441-1","DOIUrl":"https://doi.org/10.1007/s40993-023-00441-1","url":null,"abstract":"<p><p>We investigate generalizations along the lines of the Mordell-Lang conjecture of the author's <i>p</i>-adic formal Manin-Mumford results for <i>n</i>-dimensional <i>p</i>-divisible formal groups <math><mi>F</mi></math> . In particular, given a finitely generated subgroup <math><mi>Γ</mi></math> of <math><mrow><mi>F</mi> <mo>(</mo> <msub><mover><mi>Q</mi> <mo>¯</mo></mover> <mi>p</mi></msub> <mo>)</mo></mrow> </math> and a closed subscheme <math><mrow><mi>X</mi> <mo>↪</mo> <mi>F</mi></mrow> </math> , we show under suitable assumptions that for any points <math><mrow><mi>P</mi> <mo>∈</mo> <mi>X</mi> <mo>(</mo> <msub><mi>C</mi> <mi>p</mi></msub> <mo>)</mo></mrow> </math> satisfying <math><mrow><mi>n</mi> <mi>P</mi> <mo>∈</mo> <mi>Γ</mi></mrow> </math> for some <math><mrow><mi>n</mi> <mo>∈</mo> <mi>N</mi></mrow> </math> , the minimal such orders <i>n</i> are uniformly bounded whenever <i>X</i> does not contain a formal subgroup translate of positive dimension. In contrast, we then provide counter-examples to a full <i>p</i>-adic formal Mordell-Lang result. Finally, we outline some consequences for the study of the Zariski-density of sets of automorphic objects in <i>p</i>-adic deformations. Specifically, we do so in the context of the nearly ordinary <i>p</i>-adic families of cuspidal cohomological automorphic forms for the general linear group constructed by Hida.</p>","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"9 2","pages":"34"},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10149481/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9408242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}