What does this mean: $\mathbb{Z_{q}^{n}}$? I can't understand the notation $\mathbb{Z}_{q}^{n} \times \mathbb{T}$ as defined below. As far as I know  $\mathbb{Z_{q}}$ comprises all integers modulo $q$. But with $n$ as a power symbol I can't understand it. Also: $\mathbb{R/Z}$, what does it denote?

"... $ \mathbb{T} = \mathbb{R}/\mathbb{Z} $ the additive group on reals modulo one. Denote by $ A_{s,\phi} $ the distribution on $ \mathbb{Z}^n_q \times \mathbb{T}$ ..."


You write "afaik $\mathbb Z_q$ comprises..."  You have to be careful here what is meant by this notation. There are two common options:
1) $\mathbb Z_q$ is the ring of integers module $q$. Many people think this should be better written as $\mathbb Z/q$, to avoid confusion wth 2). However it is not uncommon to write $\mathbb Z_q$.
2) The ring of $q$-adic integers, i.e. formal powerseries in $q$ with coefficients in $\mathbb Z\cap [0,q-1]$.
