Ramanujan-Type congruences for cubic partition functions

Abstract

The cubic partitions of a natural number $n$, introduced by Chan and Kim, have generating function ${\sum }_{n=0}^{\infty }a(n)q^n=\frac{1}{(q;q{)}_{\infty }(q^2;q^2{)}_{\infty }}.$ In this paper, we generalize some results of Chen-Lin, which suggest that $a(n)$ should have analogous properties of the ordinary partition function. Specifically, we show that for every non-negative integer $n$, $a(5^{4}n+547)\equiv 0(\mathrm{mod}{5}^2),a(7^{3}n+190)\equiv 0(\mathrm{mod}{7}^2),a(7^{3}n+288\equiv 0(\mathrm{mod}{7}^2)anda(7^{3}n+337)\equiv 0(\mathrm{mod}{7}^2).$

This paper has been withdrawn by the author

References in corpus (2)

• Congruences for the Number of Cubic Partitions Derived from Modular Forms
• Ramanujan congruences for a class of eta quotients