On the multiplicity of the eigenvalues of discrete tori

Bing Xie, Yigeng Zhao, Yongqiang Zhao

It is well known that the standard flat torus ${\mathbb{T}}^2={\mathbb{R}}^2/{\mathbb{Z}}^2$ has arbitrarily large Laplacian-eigenvalue multiplicities. We prove, however, that $24$ is the optima…