Congruences for the Coefficients of the Powers of the Euler Product

Julia Q. D. Du, Edward Y. S. Liu, Jack C. D. Zhao

Let $p_k(n)$ be given by the $k$-th power of the Euler Product ${\prod }_{n=1}^{\infty }(1-q^n{)}^k={\sum }_{n=0}^{\infty }{p}_k(n)q^n$. By investigating the properties of the modular equat…