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

Abstract

In [SV] and [BMb], the authors proved the existence of a so-called higher rank amplifier and in [HRRa], the authors described an explicit version of a $GL(3)$ amplifier. This article provides, for $n\geq 4$, a totally explicit $GL(n)$ amplifier and gives all the results required to use it effectively.