  We show that the multiple divisor functions of integers in invertible residue
classes modulo a prime number, as well as the Fourier coefficients of GL(N)
Maass cusp forms for all N larger than 2, satisfy a central limit theorem in a
suitable range, generalizing the case N=2 treated by E. Fouvry, S. Ganguly, E.
Kowalski and P. Michel. Such universal Gaussian behaviour relies on a deep
equidistribution result of products of hyper-Kloosterman sums.
