{"title":"卡纳德-拉塞尔猜想的顶点算子模9重述","authors":"Shunsuke Tsuchioka","doi":"10.1007/s11139-024-00895-6","DOIUrl":null,"url":null,"abstract":"<p>We reformulate the Kanade–Russell conjecture modulo 9 via the vertex operators for the level 3 standard modules of type <span>\\(D^{(3)}_{4}\\)</span>. Along the same lines, we arrive at three partition theorems which may be regarded as an <span>\\(A^{(2)}_{4}\\)</span> analog of the conjecture. Andrews–van Ekeren–Heluani have proven one of them, and we point out that the others are easily proven from their results.</p>","PeriodicalId":501430,"journal":{"name":"The Ramanujan Journal","volume":"30 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A vertex operator reformulation of the Kanade–Russell conjecture modulo 9\",\"authors\":\"Shunsuke Tsuchioka\",\"doi\":\"10.1007/s11139-024-00895-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We reformulate the Kanade–Russell conjecture modulo 9 via the vertex operators for the level 3 standard modules of type <span>\\\\(D^{(3)}_{4}\\\\)</span>. Along the same lines, we arrive at three partition theorems which may be regarded as an <span>\\\\(A^{(2)}_{4}\\\\)</span> analog of the conjecture. Andrews–van Ekeren–Heluani have proven one of them, and we point out that the others are easily proven from their results.</p>\",\"PeriodicalId\":501430,\"journal\":{\"name\":\"The Ramanujan Journal\",\"volume\":\"30 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Ramanujan Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s11139-024-00895-6\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Ramanujan Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s11139-024-00895-6","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A vertex operator reformulation of the Kanade–Russell conjecture modulo 9
We reformulate the Kanade–Russell conjecture modulo 9 via the vertex operators for the level 3 standard modules of type \(D^{(3)}_{4}\). Along the same lines, we arrive at three partition theorems which may be regarded as an \(A^{(2)}_{4}\) analog of the conjecture. Andrews–van Ekeren–Heluani have proven one of them, and we point out that the others are easily proven from their results.
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