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Sharp Endpoint Extension Inequalities for the Moment Curve on Finite Fields

Year: 2025

Type: article

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.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnaf379

Authors: Chandan Biswas, Emanuel Carneiro, Taryn C Flock, Diogo Oliveira e Silva, Betsy Stovall, James Tautges

Institutions: Indian Institute of Technology Bombay, The Abdus Salam International Centre for Theoretical Physics (ICTP), Macalester College, Instituto Superior Técnico, University of Wisconsin–Madison

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Fundação para a Ciência e a Tecnologia

OpenAlex ID: W7124461209

FWCI: 1.893

Cites: 14

Cited by: 1

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