Equivalence classes of exponential polynomials with the same set of zeros

Through several equivalence binary relations, in this paper we identify, on the one hand, groups of exponential polynomials with the same set of zeros, and on the other, groups of functional equations of the form a1f(1z) + a2f(2z) + : : : + anf(nz) = 0; z 2 C that lead to equivalent exponential polynomials with the same set of zeros.