We calculate the Euler characteristics of all of the Teichmüller curves in the moduli space of
genus two Riemann surfaces which are generated by holomorphic one-forms with a single …

We provide a systematic method to compute arithmetic sums including some previously
computed by Alaca, Besge, Cheng, Glaisher, Huard, Lahiri, Lemire, Melfi, Ou, Ramanujan …

An origami is a covering of the torus T2, possibly ramified above the origin. This objectwas
introduced by William P. Thurston and William A. Veech in 1970s. Un origami can beviewed …

This book is concerned with various topics centered around connections of quasimodular
forms with Jacobi-like forms and automorphic pseudodifferential operators and is intended …

We evaluate the convolution sums ∠'_ {l+ 135m= n} σ (l) σ (m),   ∠'_ {3l+ 45m= n} σ (l)
σ (m),  ∠'_ {5l+ 27m= n} σ (l) σ (m), ∠'_ {9l+ 15m= n} σ (l) σ (m),  ∠'_ {l+ 45m= n} σ (l) …

BILLIARDS IN L-SHAPED TABLES WITH BARRIERS Matt Bainbridge 1 Introduction atb Page
1 BILLIARDS IN L-SHAPED TABLES WITH BARRIERS Matt Bainbridge Abstract. We compute …

A square-tiled surface (STS) is a (finite, possibly branched) cover of the standard square-
torus with possible branching over exactly 1 point. Alternately, STSs can be viewed as …

Origamis are translation surfaces obtained by gluing finitely many unit squares and provide
an easy access to Teichmüller curves. In particular, their monodromy represenation can be …

We evaluate the convolution using the theory of quasimodular forms and determine the
number of representations of a positive integer n by some direct sum of the forms …

A square-tiled surface (STS) is a branched cover of the standard square torus with
branching over exactly one point. In this paper we consider a randomizing model for STSs …