Zeros of systems of exponential sums and trigonometric polynomials

Details Zeros of systems of exponential sums and trigonometric polynomials Zeros of systems of exponential sums and trigonometric polynomials

2004-01-08

arxiv.org/abs/math/0401074v1

Moscow Mathematical Journal, Vol. 6 (2006), no. 1

Mathematics

Algebraic Geometry

16 pages, 2 figures

Scientific paper

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.

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