Let $\displaystyle \{z_j\}$ be the sequence of zeros on an entire function $\displaystyle f$. We define the convergence exponent of $\displaystyle \{z_j\}$ as

$\displaystyle b=\inf\left\{\lambda>0\ \text{s.t.}\ \sum_{j=1}^{+\infty}\frac{1}{|z_j|^{\lambda}}\ \textrm{converges}\right\}$

Let $\displaystyle n(r)$ be the number of $\displaystyle z_j$'s with $\displaystyle |z_j|\leq r$. Then the following identity holds:

$\displaystyle b=\limsup_{r\rightarrow +\infty}\frac{\log{\ n(r)}}{\log{r}}$

Do you think i should use Jensen formula to prove this?