Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectra of lens spaces from 1-norm spectra of congruence lattices   To every $n$-dimensional lens space $L$, we associate a congruence lattice
$\mathcal L$ in $\mathbb Z^m$, with $n=2m-1$ and we prove a formula relating
the multiplicities of Hodge-Laplace eigenvalues on $L$ with the number of
lattice elements of a given $\|\cdot\|_1$-length in $\mathcal L$. As a
consequence, we show that two lens spaces are isospectral on functions (resp.\
isospectral on $p$-forms for every $p$) if and only if the associated
congruence lattices are $\|\cdot\|_1$-isospectral (resp.\
$\|\cdot\|_1$-isospectral plus a geometric condition). Using this fact, we
give, for every dimension $n\ge 5$, infinitely many examples of Riemannian
manifolds that are isospectral on every level $p$ and are not strongly
isospectral.

19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph