A Continuum of Small-cap Decouplings and Exponential Sums for the Moment Curve in $\mathbb{R}^4$
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911720376631296 |
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| author | Glidewell, Jacob |
| author_facet | Glidewell, Jacob |
| contents | We use the high-low method and wavepacket pruning to prove new small-cap decoupling estimates for the moment curve in $\mathbb{R}^4$. As an application, we verify a conjecture of Demeter regarding the $L^{12}$ square-root cancellation of exponential sums associated with the moment curve in $\mathbb{R}^4$. This provides a continuum of square-root cancellation estimates that connects the Vinogradov MVT in $\mathbb{R}^3$ with a result of Bourgain, related to improving the best-known estimate for the Lindelöf hypothesis. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_27065 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Continuum of Small-cap Decouplings and Exponential Sums for the Moment Curve in $\mathbb{R}^4$ Glidewell, Jacob Classical Analysis and ODEs Number Theory We use the high-low method and wavepacket pruning to prove new small-cap decoupling estimates for the moment curve in $\mathbb{R}^4$. As an application, we verify a conjecture of Demeter regarding the $L^{12}$ square-root cancellation of exponential sums associated with the moment curve in $\mathbb{R}^4$. This provides a continuum of square-root cancellation estimates that connects the Vinogradov MVT in $\mathbb{R}^3$ with a result of Bourgain, related to improving the best-known estimate for the Lindelöf hypothesis. |
| title | A Continuum of Small-cap Decouplings and Exponential Sums for the Moment Curve in $\mathbb{R}^4$ |
| topic | Classical Analysis and ODEs Number Theory |
| url | https://arxiv.org/abs/2605.27065 |