Congruences modulo 27 for cubic partition pairs

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• 作者：Bernard L.S. Lin ^{linlsjmu@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：05A17 ; 11P83
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：171
• 期：Complete
• 页码：31-42
• 全文大小：258 K

文摘

Let 1950&_mathId=si1.gif&_user=111111111&_pii=S0022314X16301950&_rdoc=1&_issn=0022314X&md5=80fd073b673319438f9f3cd71a6c610c" title="Click to view the MathML source">b(n)$b(n)$ denote the number of cubic partition pairs of n  . This paper aims to study the congruences for 1950&_mathId=si1.gif&_user=111111111&_pii=S0022314X16301950&_rdoc=1&_issn=0022314X&md5=80fd073b673319438f9f3cd71a6c610c" title="Click to view the MathML source">b(n)$b(n)$ modulo 27. We first establish three Ramanujan type congruences. Then many infinite families of congruences are presented. Finally, we propose two conjectures on the congruences for 1950&_mathId=si1.gif&_user=111111111&_pii=S0022314X16301950&_rdoc=1&_issn=0022314X&md5=80fd073b673319438f9f3cd71a6c610c" title="Click to view the MathML source">b(n)$b(n)$ modulo 1950&_mathId=si2.gif&_user=111111111&_pii=S0022314X16301950&_rdoc=1&_issn=0022314X&md5=cd47c3c14f14f38fcdbda6ff225b7325" title="Click to view the MathML source">49,81$49,81$ and 243.