# finite sum of eigenvalues asymptotics

Suppose $A$ is a self-adjoint positive elliptic differential operator acting on $M$ and let $\lambda_n,n\in\mathbb{N}$ be its eigenvalues. Is it true $$\sum_{\lambda_j\leq\lambda_n} \lambda^{\alpha}_j \cong \lambda^{\alpha+1}_n,\quad \alpha\in\mathbb{R}_+ ???$$

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