Hybrid bounds for automorphic forms on ellipsoids over number fields

TL;DR

This paper establishes upper bounds for automorphic eigenfunctions on specific arithmetic manifolds, constructed as products of spheres over number fields, advancing understanding of their spectral properties.

Contribution

It introduces new bounds for automorphic forms on quaternionic adelic quotients of products of spheres, extending previous results to more complex arithmetic manifolds.

Findings

Derived explicit upper bounds for Hecke-Laplace eigenfunctions

Analyzed automorphic forms on quaternionic adelic quotients

Extended spectral bounds to higher-dimensional arithmetic manifolds

Abstract

We prove upper bounds for Hecke-Laplace eigenfunctions on certain Riemannian manifolds of arithmetic type. The manifolds under consideration are d-fold products of 2-spheres or 3-spheres, realized as adelic quotients of quaternion algebras over totally real number fields.