An improved $L^2$ restriction theorem in finite fields
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866915287197024256 |
|---|---|
| author | Fraser, Jonathan M. Rakhmonov, Firdavs |
| author_facet | Fraser, Jonathan M. Rakhmonov, Firdavs |
| contents | Mockenhaupt and Tao (Duke 2004) proved a finite field analogue of the Stein--Tomas restriction theorem, establishing a range of $q$ for which $L^q\to L^2$ restriction estimates hold for a given measure $μ$ on a vector space over a finite field. Their result is expressed in terms of exponents that describe uniform bounds on the measure and its Fourier transform. We generalise this result by replacing the uniform bounds on the Fourier transform with suitable $L^p$ bounds, and we show that our result improves upon the Mockenhaupt--Tao range in many cases. We also provide a number of applications of our result, including to Sidon sets and Hamming varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09293 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An improved $L^2$ restriction theorem in finite fields Fraser, Jonathan M. Rakhmonov, Firdavs Combinatorics Classical Analysis and ODEs Number Theory primary: 42B10, 42B05, secondary: 42B20, 28A75 Mockenhaupt and Tao (Duke 2004) proved a finite field analogue of the Stein--Tomas restriction theorem, establishing a range of $q$ for which $L^q\to L^2$ restriction estimates hold for a given measure $μ$ on a vector space over a finite field. Their result is expressed in terms of exponents that describe uniform bounds on the measure and its Fourier transform. We generalise this result by replacing the uniform bounds on the Fourier transform with suitable $L^p$ bounds, and we show that our result improves upon the Mockenhaupt--Tao range in many cases. We also provide a number of applications of our result, including to Sidon sets and Hamming varieties. |
| title | An improved $L^2$ restriction theorem in finite fields |
| topic | Combinatorics Classical Analysis and ODEs Number Theory primary: 42B10, 42B05, secondary: 42B20, 28A75 |
| url | https://arxiv.org/abs/2505.09293 |