Some congruences for 12-colored generalized Frobenius partitions


主讲人:崔素平 青海师范大学教授


地点:Tencent会议 882 831 575


主讲人先容:崔素平,中共党员,青海师范大学教授。青海省数学会副秘书长。曾获南开大学优秀毕业生、钟家庆数学奖等荣誉称号。一直从事组合及其应用等方向的研究, 主要涉及同余式、仿 theta 函数、分拆的秩等。在《Advances in Mathematics》、《Advances in Applied Mathematics》、《The Ramanujan Journal》、《International Journal of Number Theory》、《Journal of the Australian Mathematical Society》等重要期刊发表或接受发表论文21篇。

内容先容:In his 1984 AMS Memoir, Andrews introduced the family of functions $c\phi_k(n)$, the number of k-colored generalized Frobenius partitions of n. In 2019, Chan, Wang and Yang systematically studied the arithmetic properties of $\textrm{C}\Phi_k(q)$ for $2\leq k\leq17$ by utilizing the theory of modular forms, where $\textrm{C}\Phi_k(q)$ denotes the generating function of $c\phi_k(n)$. In this talk, we first establish another expression of $\textrm{C}\Phi_{12}(q)$, then prove some congruences modulo small powers of 3 for $c\phi_{12}(n)$ by using some parameterized identities of theta functions due to A. Alaca, S. Alaca and Williams. Finally, we also conjecture three families of congruences modulo powers of 3 satisfied by $c\phi_{12}(n)$.

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