Year: 2026
Type: preprint
Abstract: For each integer $k\ge3$, we establish the following estimate for all $1\le p<\infty$ and $\varepsilon>0$: \[ \left\|\sup_{t\in\mathbb{T}}\left|\sum_{n=1}^N e(nx+n^kt)\right|\right\|_{L^p(\mathbb{T})} \ll_{k,p,\varepsilon} N^{\max\{1-1/K_k,\,1-1/p\}+\varepsilon}, \] where $K_k=\min\{2^{k-1},k(k+1)/2\}$, $e(z)=e^{2πiz}$, and $\mathbb{T}=\mathbb{R}/\mathbb{Z}$. For $k\ge5$, this improves our earlier bound \cite{chen-miao-yuan-zhao} for $1\le p
Source: arXiv (Cornell University)
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222964196