On the Hodge spectra of lens spaces

Problem's Description

In [1], R. Miatello suggests the following problems:

1) Construct congruence lattices which are norm$_1$ and norm$_1*$- isospectral in all dimensions (see [2]).

2) Are there families of $p$-isospectral lens spaces for all $p$, with more than two elements?

3) Give a procedure to go from $p$-isospectral lens spaces (for all $p$) of dimension $m$ to dimension $m + 1$.

4) Establish connections with toric geometry (see [3]).

1. ArticleIs an originA list of open problems in differential geometry

   • Frank Morgan,
   • Pierre Pansu

   São Paulo Journal of Mathematical Sciences 15, 305-321, 2021fulltext

2. Article Spectra of lens spaces from 1-norm spectra of congruence lattices

   • Emilio A. Lauret,
   • Roberto J. Miatello,
   • Juan Pablo Rossetti

   International Mathematics Research Notices. IMRN, 1054-1089, 2016fulltext

3. Article On a relation between spectral theory of lens spaces and Ehrhart theory

   • B. Honari,
   • H. Mohades

   Koninklijke Nederlandse Akademie van Wetenschappen. Indagationes Mathematicae. New Series 28, 556-565, 2017fulltext