English(EN) A solution to the Erd\H{o}s Problem #1040

数学家通过新的 Lemniscate 面积证明解决了 Erdős 问题 #1040

作者 PulseAugur 编辑部 · [1 个来源] · 2026-09-10 04:00

一项新的数学证明解决了关于复平面上紧集相关 Lemniscate 面积的 Erdős 问题 #1040。该解证明，对于任何容量为 1 的紧集 K，相关单位 Lemniscate 的平面面积的下确界为零。这一结果将先前关于光滑边界集的研究扩展到任意紧集，有效地回答了一个长期存在的数学问题。 AI

排序理由该集群包含一篇提交的学术论文，详细介绍了某个数学问题的证明。[lever_c_demoted from research: ic=1 ai=0.1]

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arXiv cs.AI TIER_1 English(EN) · Ioannis Tzachristas · 2026-09-10 04:00

Erd\H{o}s问题 #1040 的一个解

arXiv:2609.06050v1 Announce Type: cross Abstract: For a compact set $K\subset\mathbb{C}$, let $\vartheta(K)$ be the infimum of the planar areas of the unit lemniscates of all monic polynomials with zeros in $K$, allowing arbitrary degree and repeated zeros. We prove that $\varthe…