TL;DR
This paper provides an intrinsic estimate for the number of connected components of the complement of an exponential sum's amoeba, improving previous bounds in both polynomial and exponential cases.
Contribution
It introduces a new intrinsic estimate for the amoeba complement components, extending and refining prior results by Forsberg, Passare, Tsikh, and Ronkin.
Findings
Improved bounds on the number of amoeba complement components.
Extension of results from polynomial to exponential sums.
Enhanced understanding of amoeba geometry in exponential sums.
Abstract
We give an intrinsic estimate of the number of connected components of the complementary set to the amoeba of an exponential sum with real spectrum improving the result of Forsberg, Passare and Tsikh in the polynomial case and that of Ronkin in the exponential one.
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