
convergence exponent
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?

Re: convergence exponent
don't know if Jensen would help or not, but the proof that I have seen uses formula
$\displaystyle \sum \frac{1}{z_j^\lambda} = \int_0^\infty \frac{dn(t)}{t^\lambda}$