  Automorphic distributions for SL(2) arise as boundary values of modular forms
and, in a more subtle manner, from Maass forms. In the case of modular forms of
weight one or of Maass forms, the automorphic distributions have continuous
first antiderivatives. We recall earlier results of one of us on the Holder
continuity of these continuous functions and relate them to results of other
authors; this involves a generalization of classical theorems on Fourier series
by S. Bernstein and Hardy-Littlewood. We then show that the antiderivatives are
non-differentiable at all irrational points, as well as all, or in certain
cases, some rational points. We include graphs of several of these functions,
which clearly display a high degree of oscillation. Our investigations are
motivated in part by properties of "Riemann's nondifferentiable function", also
known as "Weierstrass' function".
