2 problems

Let $d\geq 2$. Let $\Gamma_d(\lambda)$ denote the maximal order of vanishing of a Laplacian eigenfunction on the $d$-dimensional torus with frequency parameter $\lambda$, and let…

Let $(M,g)$ be a compact smooth manifold without boundary. Let $u$ be a Laplacian eigenfunction with eigenvalue $\lambda$, and let $p_t(x)$ be globally defined with respect to its…