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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.14937 |
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Table of Contents:
- We prove that for any $ε>0$ and any trigonometric polynomial $f$ with frequencies in the set $\{n^3: N \leq n\leq N+N^{2/3-ε}\}$, one has $$ \|f\|_4 \ll ε^{-1/4}\|f\|_2 $$ with implied constant being absolute. We also show that the set $\{n^3: N\leq n\leq N+(0.5N)^{1/2}\}$ is a Sidon set.