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

TL;DR

This paper constructs an explicit $GL(n)$ amplifier for automorphic forms, extending previous work on higher rank amplifiers and providing tools for effective application in automorphic form analysis.

Contribution

It introduces a completely explicit $GL(n)$ amplifier for all $n \\geq 4$, building on prior theoretical and $GL(3)$ explicit constructions.

Findings

Provides a fully explicit construction of the $GL(n)$ amplifier for $n \\geq 4$

Lays out all necessary results for effective use of the amplifier

Extends previous higher rank amplifier results to larger $n$

Abstract

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 $n\geq 4$, a totally explicit $GL(n)$ amplifier and gives all the results required to use it effectively.