Harmonic Maass form (original) (raw)

In mathematics, a weak Maass form is a smooth function on the upper half plane, transforming like a modular form under the action of the modular group, being an eigenfunction of the corresponding hyperbolic Laplace operator, and having at most linear exponential growth at the cusps. If the eigenvalue of under the Laplacian is zero, then is called a harmonic weak Maass form, or briefly a harmonic Maass form. A weak Maass form which has actually moderate growth at the cusps is a classical Maass wave form.