Corpus ID: 212414973

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

  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},
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
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