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P\'{o}lya's conjecture on $\mathbb{S}^1 \times \R$

math.SP · 2025-06-04 · conditional · novelty 7.0

For cylindrical strips S^1×[0,h], Pólya's conjecture holds exactly for h in (0,≈3.048] ∪ [≈3.238,≈4.046] ∪ [≈4.082,π^2/2], failing only for the 8th and 13th eigenvalues in two narrow gaps.

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  • P\'{o}lya's conjecture on $\mathbb{S}^1 \times \R$ math.SP · 2025-06-04 · conditional · none · ref 1

    For cylindrical strips S^1×[0,h], Pólya's conjecture holds exactly for h in (0,≈3.048] ∪ [≈3.238,≈4.046] ∪ [≈4.082,π^2/2], failing only for the 8th and 13th eigenvalues in two narrow gaps.