Orbitwise countings in H(2) and quasimodular forms

Abstract

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.

22 pages, 6 figures

References in corpus (1)

• Evaluating convolutions of divisor sums with quasimodular forms

Cited by in corpus (10)

• Euler characteristics of Teichmüller curves in genus two
• Evaluating convolutions of divisor sums with quasimodular forms
• Quasimodular forms, Jacobi-like forms, and pseudodifferential operators
• Siegel-Veech constants in H(2)
• Teichmüller curves in genus two: Square-tiled surfaces and modular curves
• Statistics of Square-tiled Surfaces: Symmetry and Short Loops
• Symmetric tensor representations,quasimodular forms, and weak Jacobi forms
• Billiards in L-shaped tables with barriers
• Cutting out arithmetic Teichmueller curves in genus two via Theta functions
• Dirichlet series of Rankin-Cohen Brackets