{"title":"奇部配分函数下Andrews偶部的同余模4","authors":"Dandan Chen, Rong Chen","doi":"10.1007/s00026-023-00645-3","DOIUrl":null,"url":null,"abstract":"<div><p>We find and prove a class of congruences modulo 4 for Andrews’ partition with certain ternary quadratic form. We also discuss distribution of <span>\\(\\overline{\\mathcal{E}\\mathcal{O}}(n)\\)</span> and further prove that <span>\\(\\overline{\\mathcal{E}\\mathcal{O}}(n)\\equiv 0\\pmod 4\\)</span> for almost all <i>n</i>. This study was inspired by similar congruences modulo 4 in the work by the second author and Garvan.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Congruence Modulo 4 for Andrews’ Even Parts Below Odd Parts Partition Function\",\"authors\":\"Dandan Chen, Rong Chen\",\"doi\":\"10.1007/s00026-023-00645-3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We find and prove a class of congruences modulo 4 for Andrews’ partition with certain ternary quadratic form. We also discuss distribution of <span>\\\\(\\\\overline{\\\\mathcal{E}\\\\mathcal{O}}(n)\\\\)</span> and further prove that <span>\\\\(\\\\overline{\\\\mathcal{E}\\\\mathcal{O}}(n)\\\\equiv 0\\\\pmod 4\\\\)</span> for almost all <i>n</i>. This study was inspired by similar congruences modulo 4 in the work by the second author and Garvan.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-03-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00026-023-00645-3\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00026-023-00645-3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Congruence Modulo 4 for Andrews’ Even Parts Below Odd Parts Partition Function
We find and prove a class of congruences modulo 4 for Andrews’ partition with certain ternary quadratic form. We also discuss distribution of \(\overline{\mathcal{E}\mathcal{O}}(n)\) and further prove that \(\overline{\mathcal{E}\mathcal{O}}(n)\equiv 0\pmod 4\) for almost all n. This study was inspired by similar congruences modulo 4 in the work by the second author and Garvan.
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