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We estimate the number of integers up to $x$ whose $y$-friable component exceeds $z$. Uniformly for $\max\{2,\log z\}\leqslant y\leqslant z\leqslant x/2$, we determine the logarithm of this counting function up to an error $O(\log z/\log y)$. This sharpens an estimate arising from a problem in Ford's sieve methods lect...
We study weighted Fourier extension estimates for the truncated cone. Building on the framework of Du--Li--Wang--Zhang, we introduce a more refined trilinear estimate. We obtain this estimate by applying weighted bilinear restriction on half-scale cubes and combining tube traversal with trilinear Kakeya to sum the loca...
We study Fourier extension estimates for the truncated cone in $\R^{n+1}$ with weights satisfying an $m$-dimensional ball condition only at radii between $1$ and $R^{1/2}$, where $0<m\le n-1$. Within the discrete induction framework of Du--Li--Wang--Zhang, we obtain a family of bounds by combining multilinear refined S...
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