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arXiv · 2508.08377

Sharp endpoint extension inequalities for the moment curve on finite fields

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

We investigate the sharp endpoint extension inequality for the moment curve in finite fields. We determine the optimal constant and characterize the maximizers in two complementary regimes: (i) low dimensions $d\leq 20$; (ii) large field cardinality $q\geq \frac{d(d-1)}{2 \log 6} + \frac{(2d-1)}{3}$. Our proof strategy relies on an intriguing interplay between analysis, algebra and combinatorics.

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Chandan Biswas, Emanuel Carneiro, Taryn C. Flock, Diogo Oliveira e Silva, Betsy Stovall, James Tautges. 2025-08-11. Sharp endpoint extension inequalities for the moment curve on finite fields. https://arxiv.org/abs/2508.08377

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