Counting integer points by Teichmüller discs in $\Omega\mathcal{M}(2)$

Samuel Lelièvre (1, 2) , Emmanuel Royer (1)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 IML - Institut de mathématiques de Luminy

We prove formulae for the countings by orbit of square-tiled surfaces of genus two with one singularity. These formulae were conjectured by Hubert & Lelièvre. We show that these countings admit quasimodular forms as generating functions.

Mots clés: Teichmüller discs; square-tiled surfaces; Weierstrass points; quasimodular forms

Domaines: Topologie géométrique [math.GT]; Théorie des nombres [math.NT]

Samuel Lelièvre, Emmanuel Royer. Counting integer points by Teichmüller discs in $\Omega\mathcal{M}(2)$. 2005. ⟨hal-00008577v1⟩