Exponential sums over Möbius convolutions with applications to partitions

Debmalya Basak, Nicolas Robles, Alexandru Zaharescu

We consider partitions $p_w(n)$ of a positive integer $n$ arising from the generating functions \[ \sum_{n=1}^\infty p_{w}(n) z^n = \prod_{m \in \mathbb{N}} (1-z^m)^{-w(m)}, \] w…