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arXiv · 1601.04256

On a Relation between Spectral Theory of Lens Spaces and Ehrhart Theory

H. Mohades·B. Honari
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Abstract

In this article Ehrhart quasi-polynomials of simplices are employed to determine isospectral lens spaces in terms of a finite set of numbers. Using the natural lattice associated with a lens space the associated toric variety of a lens space is introduced. It is proved that if two lens spaces are isospectral then the dimension of global sections of powers of a natural line bundle on these two toric varieties are equal and they have the same general intersection number. Also, harmonic polynomial representation of the group SO(n) is used to provide a direct proof for a theorem of Lauret, Miatello and Rossetti on isospectrality of lens spaces.

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H. Mohades, B. Honari. 2016-01-17. On a Relation between Spectral Theory of Lens Spaces and Ehrhart Theory. https://arxiv.org/abs/1601.04256

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