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Source labels openErdős Problems · Several complex variables

Erdős Problem 1041

Let f(z)=∏i=1n(z−zi)∈C[x]f(z) = \prod_{i=1}^{n} (z - z_i) \in \mathbb{C}[x] with ∣zi∣<1|z_i| < 1 for all ii.

Conjecture: Must there always exist a path of length less than 2 in {z∈C∣∣f(z)∣<1}\{ z \in \mathbb{C} \mid |f(z)| < 1 \} which connects two of the roots of ff?

Source checked Jul 26, 20261 pinned Lean statementInspect problem
Source labels openMathOverflow · Several complex variables

Mathoverflow 1973

Does the 6-sphere admit a complex structure, i.e. an atlas of holomorphically compatible charts relating it to EuclideanSpace ℂ (Fin 3)?

Source checked Jul 26, 20261 pinned Lean statementInspect problem