AlphaEvolve problems·alphaevolve:57
Rudin problem for polynomials
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Let $d \\geq 2$ and $D \\geq 1$. For $p \\in \\{4,\\infty\\}$, let $C^p(d,D)$ be the maximum of the ratio $$ \\frac{\\|u\\|_{L^p({\\mathbb S}^d)}}{\\|u\\|_{L^2({\\mathbb S}^d)}}$$ where $u$ ranges over (real) spherical harmonics of degree $D$ on the $d$-dimensional sphere $\\mathbb S^d$, which we normalize to have unit measure. Establish upper and lower bounds on $C^p(d,D)$ that are as strong as possible.
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qed.bot, “Rudin problem for polynomials”, https://qed.bot/t/alphaevolve-57, as of 30 Sep 2026.