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Intermediate-Range Estimates for Short Weyl Sums and Waring's Problem with Almost Proportional Summands
We obtain a uniform pointwise estimate for short Weyl sums of degree $n\geq3$ in the intermediate rational-approximation range $$ \frac{1}{qx^{n-2}y}\ll|λ| \ll\frac{1}{qy^{n-1}}. $$ This range arises from a second application of Dirichlet's rational approximation theorem in estimating the residual i
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