Automorphic distributions are distributions on ${\mathbb{R}}^{d}$, invariant under the linear
action of the group $SL(d,\mathbb{Z})$. Combs are characterized by the additional
requirement of being measures supported in ${\mathbb{Z}}^{d}$: their decomposition into
homogeneous components involves the family ${\left({\U0001d508}_{i\lambda}^{d}\right)}_{\lambda \in \mathbb{R}}$, of Eisenstein distributions, and the coefficients of the decomposition are given as
Dirichlet series $\mathcal{D}\left(s\right)$. Functional equations of the usual (Hecke) kind relative
to $\mathcal{D}\left(s\right)$ turn out to be equivalent to the invariance of the comb under some
modification...