Automorphy of m-fold tensor products of GL(2)

TL;DR

This paper proves that for any m-tuple of level 1 Hecke eigenforms with regular weights, there exists a self-dual automorphic form on GL(2^m) whose Galois representations match the tensor product of the forms' Galois representations.

Contribution

It establishes the automorphy of the m-fold tensor product of GL(2) automorphic forms, extending the understanding of automorphic forms on higher rank groups.

Findings

Existence of a self-dual automorphic form on GL(2^m) for given tensor products.

Correspondence between Galois representations of the automorphic form and tensor products.

Generalization of automorphy results to higher tensor powers.

Abstract

We prove that for any m > 1 given any m-tuple of Hecke eigenforms $f_i$ of level 1 whose weights satisfy the usual regularity condition there is a self-dual cuspidal automorphic form $\pi$ of $\GL_{2^m}(\Q)$ corresponding to their tensor product, i.e., such that the system of Galois representations attached to $\pi$ agrees with the tensor product of the ones attached to the cuspforms $f_i$.