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arXiv · 2609.29882

Sharp endpoint extension inequalities for the moment curve on finite fields II: an extremal property of the uniform distribution

Chandan Biswas·Emanuel Carneiro·Taryn C. Flock·José Madrid·Diogo Oliveira e Silva·Betsy Stovall·James Tautges
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Abstract

We identify the optimal constant and describe all maximizers for the Fourier endpoint extension inequality associated with the moment curve over finite fields. This confirms a conjecture proposed in the authors' earlier work. The proof proceeds by showing that the problem is equivalent to a purely probabilistic extremal statement: among all probability distributions on a finite set, the uniform distribution uniquely maximizes the expected number of distinct rearrangements of an i.i.d. sample.

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Chandan Biswas, Emanuel Carneiro, Taryn C. Flock, José Madrid, Diogo Oliveira e Silva, Betsy Stovall, James Tautges. 2026-09-24. Sharp endpoint extension inequalities for the moment curve on finite fields II: an extremal property of the uniform distribution. https://arxiv.org/abs/2609.29882

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