Character sums over smooth numbers

Seth Hardy, Max Wenqiang Xu

Let $\Psi (x,y)$ denote the count of $y$-smooth numbers below $x$ and $P(n)$ denote the largest prime factor of $n$. We show that \[ \frac{1}{φ(q)} \sum_{χ\bmod q} \Bigl| \sum_{\substa…