Sharp endpoint extension inequalities for the moment curve on finite fields
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908484981751808 |
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| author | Biswas, Chandan Carneiro, Emanuel Flock, Taryn C. Silva, Diogo Oliveira e Stovall, Betsy Tautges, James |
| author_facet | Biswas, Chandan Carneiro, Emanuel Flock, Taryn C. Silva, Diogo Oliveira e Stovall, Betsy Tautges, James |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_08377 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp endpoint extension inequalities for the moment curve on finite fields Biswas, Chandan Carneiro, Emanuel Flock, Taryn C. Silva, Diogo Oliveira e Stovall, Betsy Tautges, James Classical Analysis and ODEs Combinatorics 42B10 (Primary), Secondary: 12E20, 05C70, 05B25, 26D15, 05E05 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. |
| title | Sharp endpoint extension inequalities for the moment curve on finite fields |
| topic | Classical Analysis and ODEs Combinatorics 42B10 (Primary), Secondary: 12E20, 05C70, 05B25, 26D15, 05E05 |
| url | https://arxiv.org/abs/2508.08377 |