The asymptotic number of maps on compact orientable surfaces

We get an asymptotic formula for the sum
$$ Z_{N}=\sum_{b+p=N}F_{b,p}y^p, $$
where
$$ F_{b,p}=\sum_{\rho=0}^\infty F_{b,p}(\rho), $$
and $F_{b,p}(\rho)$ is the number of maps of genus $\rho$ with $p+1$ vertices and $p+b$ edges.