Maass forms

Maass forms are special functions in mathematics that exist on the surface of a geometric shape called the hyperbolic plane. They are solutions to certain differential equations and have symmetrical properties when transformed in specific ways. Unlike typical functions, Maass forms are not necessarily smooth or periodic but display a consistent pattern of behavior under these transformations. They play a key role in areas like number theory and quantum chaos, helping mathematicians understand deep connections between geometry, symmetry, and numbers.