Number Theory

Description:  This is a plot of a Maass waveform for the group SL_2(Z). A Maass waveform is a highly symmetric function which has connections to number theory. These functions are periodic, so they are expressed as Fourier series. Their domain is the complex upper half-plane, and the Fourier series involves a K-Bessel function applied to the imaginary part of the input. Maass forms can also be understood as (time-independent) solutions to the problem of computing quantum energy states of a particle on a surface or in a 3D region. These functions are computed numerically using a method known as Hejhal's algorithm.