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PreprintarXiv licencearXiv

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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Cite

BibTeXRIS
BibTeX
@misc{biswas2026sharp,
  title = {{Sharp endpoint extension inequalities for the moment curve on finite fields II: an extremal property of the uniform distribution}},
  author = {Chandan Biswas and Emanuel Carneiro and Taryn C. Flock and José Madrid and Diogo Oliveira e Silva and Betsy Stovall and James Tautges},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.29882},
  eprint = {2609.29882},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.29882},
}
RIS
TY  - UNPB
TI  - Sharp endpoint extension inequalities for the moment curve on finite fields II: an extremal property of the uniform distribution
AU  - Chandan Biswas
AU  - Emanuel Carneiro
AU  - Taryn C. Flock
AU  - José Madrid
AU  - Diogo Oliveira e Silva
AU  - Betsy Stovall
AU  - James Tautges
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.29882
UR  - https://arxiv.org/abs/2609.29882
AB  - 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.
ER  -