Double square moments and bounds for resonance sums of cusp forms

Tim Gillespie, Praneel Samanta, Yangbo Ye

Let $f$ and $g$ be holomorphic cusp forms for the modular group $S{L}_2(\mathbb{Z})$ of weight $k_1$ and $k_2$ with Fourier coefficients ${\lambda }_f(n)$ and ${\lambda }_g(n)$, respectively. For real…