An Analogue of the Dedekind Eta Function for Hecke Groups

Let D ≡ 1 mod 4 be a fundamental discriminant of a real quadratic field. We will construct an analogue of the classical Dedekind eta function for Hecke groups, giving rise to a family of holomorphic modular functions that vanish at the cusp at infinity. If time permits, we will discuss the asymptotic growth and sign patterns of the Fourier coefficients of these modular functions.