AlphaEvolve problems·alphaevolve:57

Rudin problem for polynomials

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 p

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