Real zeros of SONC polynomials

We provide a complete and explicit characterization of the real zeros of sums of nonnegative circuit (SONC) polynomials, a recent certificate for nonnegative polynomials independent of sums of squares. As a consequence, we derive an exact determination of the number Bn+1,2d″ for all n and d. Bn+1,2d″ is defined to be the supremum of the number of zeros of all homogeneous n+1-variate polynomials of degree 2d in the SONC cone. The analogously defined numbers Bn+1,2d and Bn+1,2d′ for the nonnegativity cone and the cone of sums of squares were first introduced and studied by Choi, Lam, and Reznick. In strong contrast to our case, the determination of both Bn+1,2d and Bn+1,2d′ for general n and d is still an open question.