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 Mosc. Math. J., 2006, Volume 6, Number 1, Pages 153–168 (Mi mmj241)

Zeros of systems of exponential sums and trigonometric polynomials

E. Soprunova

Department of Mathematics and Statistics, University of Massachusetts

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 $(\mathbb C^{\times})n$ whose Newton polytopes 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.

Key words and phrases: Exponential sums, trigonometric polynomials, quasiperiodic functions, mean value.

DOI: https://doi.org/10.17323/1609-4514-2006-6-1-153-168

Full text: http://www.ams.org/.../abst6-1-2006.html
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Bibliographic databases:

MSC: 14P15, 33B10
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Citation: E. Soprunova, “Zeros of systems of exponential sums and trigonometric polynomials”, Mosc. Math. J., 6:1 (2006), 153–168

Citation in format AMSBIB
\Bibitem{Sop06} \by E.~Soprunova \paper Zeros of systems of exponential sums and trigonometric polynomials \jour Mosc. Math.~J. \yr 2006 \vol 6 \issue 1 \pages 153--168 \mathnet{http://mi.mathnet.ru/mmj241} \crossref{https://doi.org/10.17323/1609-4514-2006-6-1-153-168} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2265953} \zmath{https://zbmath.org/?q=an:1132.14048} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000208595700010} 

• http://mi.mathnet.ru/eng/mmj241
• http://mi.mathnet.ru/eng/mmj/v6/i1/p153

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Soprunova E., “Exponential Gelfond-Khovanskii formula in dimension one”, Proc. Amer. Math. Soc., 136:1 (2008), 239–245
2. A. I. Èsterov, “Densities of topological invariants of quasi-periodic subanalytic sets”, Izv. Math., 73:3 (2009), 611–626