  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.

Differential Geometry;Algebraic Geometry