  Gelfond and Khovanskii found a formula for the sum of the values of a Laurent
polynomial at the zeros of a system of n Laurent polynomials in the complex
n-torus whose Newton polyhedra have generic mutual positions. An exponential
change of variables gives a similar formula for exponential sums with rational
frequencies. We conjecture that this formula holds for exponential sums with
real frequencies. We give an integral formula which proves the existence-part
of the conjectured formula not only in the complex situation but also in a very
general real setting. We also prove the conjectured formula when it gives
answer zero, which happens in most cases.
