Most A$_α$-eigenvalues of a tree are small

We study the distribution of $A_α$-eigenvalues of a tree. We extend the works \cite{Jacobs2021} and \cite{SIN2020} by proving that the number of $A_α$-eigenvalues, for $0\leq α\leq \frac{1}{2}$, less than or equal to the average degree $d_α= α(2- 2/n)$ is, at least, $\lceil \frac{n}{2} \rceil$ for a