2 problems

Let … be an eta-quotient shifted so that all powers of $q$ are integral, and let $\delta_F$ be the odd density of its coefficients $c(n)$, when this density exists. A polynomial is…

Let $b_m(n)$ be the coefficients of the generating function for $m$-regular partitions. For even $m$, write … where $m_0$ is odd. The odd density of a sequence is the limiting prop…