Mathematics > Classical Analysis and ODEs
arXiv:2606.01447 (math)
[Submitted on 31 May 2026]
Abstract:For real multivariate polynomials $P$ and $Q$ both vanishing at a point, if the zero set of $Q$ is contained in the zero set of $P$, then there exists a rational function of the form $P^{p}/Q^{q}$ which is locally bounded and such that its extension that vanishes on the zero set of $Q$ is discontinuous. The proof uses inequalities of Lojasiewicz.
Submission history
From: Adam Coffman [view email]
[v1]
Sun, 31 May 2026 20:48:24 UTC (1,230 KB)
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