Pub Date : 2023-01-01DOI: 10.1007/s40993-023-00433-1
Cameron Franc, Geoffrey Mason
We postulate axioms for a chiral half of a nonarchimedean 2-dimensional bosonic conformal field theory, that is, a vertex operator algebra in which a p-adic Banach space replaces the traditional Hilbert space. We study some consequences of our axioms leading to the construction of various examples, including p-adic commutative Banach rings and p-adic versions of the Virasoro, Heisenberg, and the Moonshine module vertex operator algebras. Serre p-adic modular forms occur naturally in some of these examples as limits of classical 1-point functions.
{"title":"<i>p</i>-adic vertex operator algebras.","authors":"Cameron Franc, Geoffrey Mason","doi":"10.1007/s40993-023-00433-1","DOIUrl":"https://doi.org/10.1007/s40993-023-00433-1","url":null,"abstract":"<p><p>We postulate axioms for a chiral half of a nonarchimedean 2-dimensional bosonic conformal field theory, that is, a vertex operator algebra in which a <i>p</i>-adic Banach space replaces the traditional Hilbert space. We study some consequences of our axioms leading to the construction of various examples, including <i>p</i>-adic commutative Banach rings and <i>p</i>-adic versions of the Virasoro, Heisenberg, and the Moonshine module vertex operator algebras. Serre <i>p</i>-adic modular forms occur naturally in some of these examples as limits of classical 1-point functions.</p>","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"9 2","pages":"27"},"PeriodicalIF":0.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10071837/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9289144","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}
{"title":"Kampé de Fériet hypergeometric functions over finite fields","authors":"Ryojun Ito, Satoshi Kumabe, Akio Nakagawa, Yusuke Nemoto","doi":"10.1007/s40993-023-00460-y","DOIUrl":"https://doi.org/10.1007/s40993-023-00460-y","url":null,"abstract":"","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"25 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90279150","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}
Pub Date : 2022-12-12DOI: 10.1007/s40993-022-00407-9
D. Lubicz, Damien Robert
{"title":"Fast change of level and applications to isogenies","authors":"D. Lubicz, Damien Robert","doi":"10.1007/s40993-022-00407-9","DOIUrl":"https://doi.org/10.1007/s40993-022-00407-9","url":null,"abstract":"","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"26 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81124136","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}
Pub Date : 2022-11-29DOI: 10.1007/s40993-022-00395-w
Juanita Duque-Rosero, J. Voight
{"title":"Triangular modular curves of small genus","authors":"Juanita Duque-Rosero, J. Voight","doi":"10.1007/s40993-022-00395-w","DOIUrl":"https://doi.org/10.1007/s40993-022-00395-w","url":null,"abstract":"","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"285 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72443235","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}
Pub Date : 2022-11-29DOI: 10.1007/s40993-022-00416-8
Zafer Selcuk Aygin
{"title":"Rogers–Ramanujan type generalized reciprocal identities and Eisenstein series","authors":"Zafer Selcuk Aygin","doi":"10.1007/s40993-022-00416-8","DOIUrl":"https://doi.org/10.1007/s40993-022-00416-8","url":null,"abstract":"","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"1 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88716266","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}
Pub Date : 2022-11-10DOI: 10.1007/s40993-023-00442-0
Fabien Cl'ery, G. van der Geer
{"title":"Modular forms via invariant theory","authors":"Fabien Cl'ery, G. van der Geer","doi":"10.1007/s40993-023-00442-0","DOIUrl":"https://doi.org/10.1007/s40993-023-00442-0","url":null,"abstract":"","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"47 1","pages":"1-10"},"PeriodicalIF":0.8,"publicationDate":"2022-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80664305","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}
Pub Date : 2022-11-07DOI: 10.1007/s40993-023-00429-x
J. Müller, Berno Reitsma
{"title":"Computing torsion subgroups of Jacobians of hyperelliptic curves of genus 3","authors":"J. Müller, Berno Reitsma","doi":"10.1007/s40993-023-00429-x","DOIUrl":"https://doi.org/10.1007/s40993-023-00429-x","url":null,"abstract":"","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"23 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80787292","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}
Pub Date : 2022-10-26DOI: 10.1007/s40993-022-00406-w
Barinder S. Banwait
{"title":"Correction: Examples of abelian surfaces failing the local-global principle for isogenies","authors":"Barinder S. Banwait","doi":"10.1007/s40993-022-00406-w","DOIUrl":"https://doi.org/10.1007/s40993-022-00406-w","url":null,"abstract":"","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"70 1","pages":"1-3"},"PeriodicalIF":0.8,"publicationDate":"2022-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90239827","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}
Pub Date : 2022-10-25DOI: 10.1007/s40993-022-00394-x
F. Morain
{"title":"Modular curves over number fields and ECM","authors":"F. Morain","doi":"10.1007/s40993-022-00394-x","DOIUrl":"https://doi.org/10.1007/s40993-022-00394-x","url":null,"abstract":"","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"43 1","pages":"1-17"},"PeriodicalIF":0.8,"publicationDate":"2022-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87301159","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}
Pub Date : 2022-10-22DOI: 10.1007/s40993-022-00403-z
Guodong Hua
{"title":"The average behaviour of Hecke eigenvalues over certain sparse sequence of positive integers","authors":"Guodong Hua","doi":"10.1007/s40993-022-00403-z","DOIUrl":"https://doi.org/10.1007/s40993-022-00403-z","url":null,"abstract":"","PeriodicalId":43826,"journal":{"name":"Research in Number Theory","volume":"39 2 1","pages":"1-20"},"PeriodicalIF":0.8,"publicationDate":"2022-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82427378","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}
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