Soon-Yi Kang (강순이), The Product and Quotient of Generating Series for Partitions and Sums of Squares

We first present how to extend Ramanujan’s method in partition congruences and show a congruence relation that the coefficients of the quotient of generating series for partitions and sums of squares satisfy. Then we observe a combinatorial interpretation of the product of them and see whether we could find some arithmetic properties of its coefficients.