Restrictions of SL_3 Maass forms to maximal flat subspaces

TL;DR

This paper improves bounds on the L^2 norm of Hecke-Maass forms restricted to flat subspaces using arithmetic amplification, advancing understanding of automorphic forms on division algebras.

Contribution

It introduces an application of arithmetic amplification to enhance local bounds for Maass forms on cubic division algebras.

Findings

Improved local bounds for L^2 norms of Maass forms

Demonstrated effectiveness of arithmetic amplification in this context

Enhanced understanding of restrictions of automorphic forms

Abstract

Let \psi be a Hecke-Maass form on a cubic division algebra over \Q. We apply arithmetic amplification to improve the local bound for the L^2 norm of \psi restricted to maximal flat subspaces.