An extension of Bohr’s equivalence theorem to the case of exponential polynomials with distinct sets of frequencies

Abstract Inspired by Bohr’s equivalence relation concerning general Dirichlet series, in this paper we introduce a new equivalence relation on certain classes of exponential polynomials whose sets of frequencies are not necessarily equal. We first characterize this equivalence relation through a new perspective, and finally we obtain an improvement of Bohr’s equivalence theorem for the case of these finite exponential sums.