Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 28 min ago
PreprintarXiv licencearXiv

Sharp L2 → L4 extension inequality for quadratic surfaces in finite fields

  • Pedro Ronda
Open at sourcePDFDOICite

Abstract

In this work, we establish the sharp L2 → L4 extension inequality for a large class of quadratic surfaces in 𝔽3, where 𝔽 is a finite field of odd characteristic. These surfaces include the cones without the origin and the spheres with nonzero radius j such that −j is not a square in 𝔽. We also show that the maximizers of these inequalities must have constant modulus.

Related

  1. p-class groups in the cyclotomic ℤp-extension of imaginary quadratic fields
    Somnath Jha, Debanjana Kundu, H. Laxmi +1
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  2. A trace Paley-Wiener theorem for GLn(F)backslash GLn(E), with E/F a quadratic extension of non-Archimedean local fields
    Juliette Coutens
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. On some Non-Permutations of Quadratic Extension of Finite Field
    Bidushi Sharma, Dhiren Kumar Basnet
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. 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 +4
    arXivPreprintarXiv licenceFull textAnalysis & PDEsProbabilityarXiv
  5. Rational Points on Danielewski Surfaces over Finite fields and Polygonal Numbers
    Sakshi Gupta, Anit Kuckian, Indranath Sengupta
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{ronda2026sharp,
  title = {{Sharp $L^2 \to L^4$ extension inequality for quadratic surfaces in finite fields}},
  author = {Pedro Ronda},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13023},
  eprint = {2609.13023},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13023},
}
RIS
TY  - UNPB
TI  - Sharp L^2 → L^4 extension inequality for quadratic surfaces in finite fields
AU  - Pedro Ronda
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.13023
UR  - https://arxiv.org/abs/2609.13023
AB  - In this work, we establish the sharp L^2 → L^4 extension inequality for a large class of quadratic surfaces in 𝔽^3, where 𝔽 is a finite field of odd characteristic. These surfaces include the cones without the origin and the spheres with nonzero radius j such that −j is not a square in 𝔽. We also show that the maximizers of these inequalities must have constant modulus.
ER  -