Compact periods of Eisenstein series of orthogonal groups of rank one

TL;DR

This paper analyzes the periods of Eisenstein series on orthogonal groups of rank one, expressing them as Euler products and explicitly evaluating local factors at odd primes, advancing understanding of automorphic forms.

Contribution

It provides a detailed decomposition of Eisenstein series periods on orthogonal groups into Euler products, including explicit local factor evaluations at odd primes.

Findings

Period integrals expressed as Euler products

Explicit evaluation of local factors at odd primes

Enhanced understanding of automorphic forms on orthogonal groups

Abstract

Let G=O(n+3) be an orthogonal group of rank one and H=O(n+2) an anisotropic subgroup. We unwind the period along H of a spherical Eisenstein series of G against a cuspform of H into an Euler product and evaluate the local factors at odd primes.