On the multivariate Fujiwara bound for exponential sums

Jens Forsgård

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arXiv · 1612.03738

On the multivariate Fujiwara bound for exponential sums

Jens Forsgård

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Abstract

We prove the multivariate Fujiwara bound for exponential sums: for a $d$-variate exponential sum $f$ with scaling parameter $\mu$, if $x$ is contained in the amoeba $\mathscr{A}(f)$, then the distance from $x$ to the Archimedean tropical variety associated to $f$ is at most $d \sqrt{d}\, 2\log(2 + \sqrt{3})/ \mu$. If $f$ is polynomial, then the bound can be improved to $d \log(2 + \sqrt{3})$.

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BibTeX RIS

Jens Forsgård. 2016-12-12. On the multivariate Fujiwara bound for exponential sums. https://arxiv.org/abs/1612.03738

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