Improved leading coefficient in the individual Berezin-Li-Yau bound via energy orthogonality

Yifan Wang, Hehu Xie

Let ${\lambda }_k$ be the $k$th eigenvalue of the Dirichlet Laplacian on an open set $\Omega \subset {\mathbb{R}}^n$ of finite positive measure. The direct individual consequence of the Berezin--Li--…