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Proceedings of the American Mathematical Society

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Exponential Gelfond-Khovanskii formula in dimension one


Author: Evgenia Soprunova
Journal: Proc. Amer. Math. Soc. 136 (2008), 239-245
MSC (2000): Primary 30C15
DOI: https://doi.org/10.1090/S0002-9939-07-09091-0
Published electronically: October 5, 2007
MathSciNet review: 2350409
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Abstract: Gelfond and Khovanskii found a formula for the sum of the values of a Laurent polynomial over the zeros of a system of $ n$ Laurent polynomials in $ (\mathbb{C}\setminus 0)^n$. We expect that a similar formula holds in the case of exponential sums with real frequencies. Here we prove such a formula in dimension one.


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Additional Information

Evgenia Soprunova
Affiliation: Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242
Email: soprunova@math.kent.edu

DOI: https://doi.org/10.1090/S0002-9939-07-09091-0
Keywords: Exponential sums, mean value, mean number of zeros
Received by editor(s): October 25, 2006
Published electronically: October 5, 2007
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.