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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

Exponential Gelfond-Khovanskii formula in dimension one

Author(s): Evgenia Soprunova
Journal: Proc. Amer. Math. Soc. 136 (2008), 239-245.
MSC (2000): Primary 30C15
Posted: October 5, 2007
MathSciNet review: 2350409
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Abstract | References | Similar articles | Additional information

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.

References:

[1]
O. Gelfond, A. Khovanskii, Newton polyhedra and Grothendieck residues (in Russian), Dokl. Akad. Nauk, 350 (1996), no. 3, 298-300. MR 1444043 (98b:32004)

[2]
O. Gelfond, A. Khovanskii, Toric geometry and Grothendieck residues, Moscow Mathematical Journal, Vol. 2 (2002), no. 1, 99-112. MR 1900586 (2003h:14074)

[3]
O. Gelfond, Zeros of systems of quasiperiodic polynomials, FIAN preprint, no. 200 (1978).

[4]
O. Gelfond, The mean number of roots of systems of holomorphic almost periodic equations. (Russian) Uspekhi Mat. Nauk 39 (1984), no. 1(235), 123-124. MR 733961 (86a:32007)

[5]
A. Khovanskii, Newton polyhedra, a new formula for mixed volume, product of roots of a system of equations, Fields Inst. Comm., Vol. 24 (1999), 325-364. MR 1733583 (2001d:52013)

[6]
A. Khovanskii, Fewnomials, A.M.S., 1991 MR 1108621 (92h:14039)

[7]
A. Khovanskii, S. Yakovenko, Generalized Rolle Theorem in $ \mathbb{R}^n$ and $ \mathbb{C}$, J. Dynam. Control Systems 2 (1996), no. 1, 103-123. MR 1377431 (97f:26016)

[8]
J. Ritt, On the zeros of exponential polynomials, Transactions of The American Mathematical Society, Vol. 31, Issue 4 (1929), 680-686. MR 1501506

[9]
E. Soprunova, Zeros of systems of exponential sums and trigonometric polynomials, Moscow Mathematical Journal, Vol. 6 (2006), no. 1. MR 2265953

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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: 10.1090/S0002-9939-07-09091-0
PII: S 0002-9939(07)09091-0
Keywords: Exponential sums, mean value, mean number of zeros
Received by editor(s): October 25, 2006
Posted: October 5, 2007
Communicated by: Juha M. Heinonen
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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