I am reading Prime arithmetic Teichmuller discs in H(2) where they discuss the Siegel-Veech constant in a stratum $\mathcal{H}(2)$ of surfaces. However I see two definitions of Siegel-Veech constant:
- $N(L)$ the number of parallel simple closed geodesics of length not exceeding $L$
In for genus greater than $1$ there are two separate definitions
$N_{cyl}(L)$ the number of maximal cylinders made from parallel closed geodesics
$N_{sc}(L)$ number of saddle connections connecting the singularities of the flat surface.
From what I gather, there are generatic Siegel Veech constants and constants for specific surfaces. Fine.
Why does this paper suggest, is it equivalent to count square-tiled surfaces of a given size?
