Voronoi summation formula for the generalized divisor function ${\sigma }_z^{(k)}(n)$

Atul Dixit, Bibekananda Maji, Akshaa Vatwani

For a fixed $z\in \mathbb{C}$ and a fixed $k\in \mathbb{N}$, let ${\sigma }_z^{(k)}(n)$ denote the sum of $z$-th powers of those divisors $d$ of $n$ whose $k$-th powers also divide $n$. Th…