We investigate the transcendental nature of the sum [Formula: see text] where A(x), B(x) are polynomials with algebraic coefficients with deg A < deg B and the sum is over integers n which are not zeros of B(x). We relate this question to the celebrated conjectures of Gel'fond and Schneider. In certain cases, these conjectures are known, and this allows us to obtain some unconditional results of a general nature.