Upper bounds for geodesic periods over hyperbolic manifolds

TL;DR

This paper establishes an upper bound for geodesic periods of Maass forms on hyperbolic manifolds, providing uniform estimates under certain conditions, which advances understanding of automorphic forms and their restrictions.

Contribution

It introduces a new upper bound for geodesic periods of Maass forms over hyperbolic manifolds, with uniform estimates under specific restrictions.

Findings

Derived an explicit upper bound for geodesic periods

Achieved uniform bounds under certain geometric restrictions

Enhanced understanding of Maass form restrictions on hyperbolic cycles

Abstract

We prove an upper bound for geodesic periods of Maass forms over hyperbolic manifolds. By definition, such periods are integrals of Maass forms restricted to a special geodesic cycle of the ambient manifold, against a Maass form on the cycle. Under certain restrictions, the bound will be uniform.