Non-strongly isospectral spherical space forms

TL;DR

This paper discusses the explicit construction of lens spaces that are isospectral on p-forms for all p but not strongly isospectral, highlighting limitations of the Sunada method and analyzing classical results through generating functions.

Contribution

It introduces new examples of lens spaces that are p-form isospectral but not strongly isospectral, beyond the scope of the Sunada method, and revisits classical work with a focus on generating functions.

Findings

Constructed lens spaces that are p-form isospectral but not strongly isospectral

Demonstrated limitations of the Sunada method for these examples

Analyzed classical results of Ikeda using generating functions

Abstract

In this paper we describe recent results on explicit construction of lens spaces that are not strongly isospectral, yet they are isospectral on $p$-forms for every $p$. Such examples cannot be obtained by the Sunada method. We also discuss related results, emphasizing on significant classical work of Ikeda on isospectral lens spaces, via a thorough study of the associated generating functions.