Period integrals of distinguished polarised strongly tempered hyperspherical varieties

TL;DR

This paper introduces new period integrals for distinguished polarized strongly tempered hyperspherical varieties, linking them to L-functions within the framework of the Relative Langlands Duality, expanding understanding of automorphic forms.

Contribution

It presents novel period integrals for a class of hyperspherical varieties and explores their connection to L-functions, advancing the theory of automorphic periods.

Findings

New period integrals linked to hyperspherical varieties

Connections established between integrals and L-functions

Enhancement of the Relative Langlands Duality framework

Abstract

Recent work of Mao, Wan and Zhang \cite{MWZ} has provided a complete list of strongly tempered hyperspherical varieties and they proposed some new period integrals. In this paper, I will present new period integrals of distinguished polarised strongly tempered hyperspherical varieties and discuss the L-functions these integrals represent, as examples of the Relative Langlands Duality.