# Tropical varieties for exponential sums

@article{Ergr2019TropicalVF,
title={Tropical varieties for exponential sums},
author={Alperen Ali Erg{\"u}r and Grigoris Paouris and J. Maurice Rojas},
journal={Mathematische Annalen},
year={2019},
pages={1-20}
}
• Published 14 December 2014
• Mathematics
• Mathematische Annalen
We study the complexity of approximating complex zero sets of certain n-variate exponential sums. We show that the real part, R, of such a zero set can be approximated by the $$(n-1)$$(n-1)-dimensional skeleton, T, of a polyhedral subdivision of $$\mathbb {R}^n$$Rn. In particular, we give an explicit upper bound on the Hausdorff distance: $$\Delta (R,T) =O\left( t^{3.5}/\delta \right)$$Δ(R,T)=Ot3.5/δ, where t and $$\delta$$δ are respectively the number of terms and the minimal spacing of the…
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