The $L^2$ restriction norm of a $GL_3$ Maass form

TL;DR

This paper establishes a precise upper bound for the $L^2$ norm of a $GL_3$ Maass form when restricted to a $GL_2$ subgroup, advancing understanding of automorphic form restrictions.

Contribution

It provides the first sharp upper bound for the restriction norm of $GL_3$ Maass forms to $GL_2$, a significant step in automorphic form analysis.

Findings

Sharp upper bound on the restriction norm is proven.

The result improves previous bounds and matches conjectural expectations.

The method involves advanced harmonic analysis and automorphic representation theory.

Abstract

We prove a sharp upper bound on the $L^2$ norm of a $GL_3$ Maass form restricted to $GL_2 \times \mathbb{R}^{+}$.