Corpus ID: 212414973

# Hybrid bounds on two-parametric family Weyl sums along smooth curves

@article{Chen2020HybridBO,
title={Hybrid bounds on two-parametric family Weyl sums along smooth curves},
author={Chang Shing Chen and Igor E. Shparlinski},
journal={arXiv: Classical Analysis and ODEs},
year={2020}
}
• Published 5 March 2020
• Mathematics
• arXiv: Classical Analysis and ODEs
We obtain a new bound on Weyl sums with degree $k\ge 2$ polynomials of the form $(\tau x+c) \omega(n)+xn$, $n=1, 2, \ldots$, with fixed $\omega(T) \in \mathbb{Z}[T]$ and $\tau \in \mathbb{R}$, which holds for almost all $c\in [0,1)$ and all $x\in [0,1)$. We improve and generalise some recent results of M.~B.~Erdogan and G.~Shakan (2019), whose work also shows links between this question and some classical partial differential equations. We extend this to more general settings of families of… Expand
1 Citations
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We show that $\bigg \|\sup _{0 < t < 1} \big |\sum _{n=1}^{N} e^{2\pi i (n(\cdot ) + n^2 t)}\big | \bigg \|_{L^{4}([0,1])} \leq C_{\epsilon } N^{3/4 + \epsilon }$ and discuss some applications toExpand

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