On correlations of CM-type Maass waveforms under the horocyclic flow

Maass waveforms of CM-type are a special kind of eigenfunction of the hyperbolic Laplacian whose 'defining' components (namely eigenvalue and Fourier coefficients) are given by simple formulae involving algebraic integers chosen from a suitable number field K/ℚ. In this paper, we report on some computer experiments aimed at ascertaining the extent to which the autocorrelation behaviour of CM-forms agrees with that of 'mock' (i.e. random) waveforms in the limit of high energy. Our results suggest that no significant differences are seen.