Uniform bounds for period integrals and sparse equidistribution

James Tanis, Pankaj Vishe

Let $M=\Gamma \backslash \mathrm{PSL}(2,\mathbb{R})$ be a compact manifold, and let $f\in C^{\infty }(M)$ be a function of zero average. We use spectral methods to get uniform (i.e. independ…