Spectra of lens spaces from 1-norm spectra of congruence lattices (Q2797852)

Two Riemannian manifolds are called \(p\)-isospectral if theirs Hodge-Laplace spectra on \(p\)-forms are the same. In this paper, the authors associate a congruence lattice in \(\mathbb{R}^{m}\) to a \((2m-1)\)-dimensional lens space, and relate the Hodge-Laplace spectrum on \(p\)-form of the Lens space to a given 1-length multiplicities of elements in the lattice. Through this connection, for every dimension \(n\geq 5\), they construct examples of Riemannian manifolds that are isospectral in every level \(p\) and are not strongly isospectral.