Zeros of systems of exponential sums and trigonometric polynomials

Evgenia Soprunova

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Zeros of systems of exponential sums and trigonometric polynomials

Evgenia Soprunova

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Abstract

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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BibTeX RIS

Evgenia Soprunova. 2004-01-08. Zeros of systems of exponential sums and trigonometric polynomials. https://arxiv.org/abs/math/0401074

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