Sharp Endpoint Extension Inequalities for the Moment Curve on Finite Fields
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 $d\leq 20$ and (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.
Authors
- Betsy Stovall (ORCID: https://orcid.org/0000-0001-6447-8386)
- Diogo Gaspar Teixeira Oliveira e Silva
- Emanuel Carneiro (ORCID: https://orcid.org/0000-0001-6229-1139)
- Taryn C. Flock (ORCID: https://orcid.org/0000-0001-8281-5980)
- Chandan Biswas (ORCID: https://orcid.org/0000-0002-1383-3218)
- James Tautges
Institutions
- Instituto de Engenharia de Sistemas e Computadores Investigação e Desenvolvimento (PT)
- The Abdus Salam International Centre for Theoretical Physics (ICTP) (IT)
- University of Wisconsin–Madison (US)
- Indian Institute of Technology Bombay (IN)
- Macalester College (US)
Publication Details
- Journal
- International Mathematics Research Notices
- Published
- 2025-12-19
- DOI
- https://doi.org/10.1093/imrn/rnaf379
- Citations
- 1
- Primary Topic
- Coding theory and cryptography
- Type
- article
- Field-Weighted Citation Impact
- 2.48