The amplification method in the context of $GL(n)$ automorphic forms

In \cite{SiVe2} and \cite{BlMa1}, the authors proved the existence of a so-called higher rank amplifier and in \cite{HoRiRo2}, the authors described an explicit version of a $GL(3)$ amplifier. This article provides, for $n\ge 4$, a totally explicit $GL(n)$ amplifier and gives all the results required to use it effectively.