6 citations · 6 across the 4 of their papers we have counts for
6 papers
Subcritical paucity and -improving estimates for finite-type polynomial curves
Kevin Hughes
I prove new subcritical bounds for the -improving problem along restricted subsets of a degenerate curve. The key input is a new paucity estimate for associated inhomogeneo…
Some subcritical estimates for the -improving problem for discrete curves
Spyridon Dendrinos, Kevin Hughes, Marco Vitturi
We apply Christ's method of refinements to the -improving problem for discrete averages along polynomial curves in . Combined with certain ele…
Supercritical discrete restriction estimates for forms in many variables
Brian Cook, Kevin Hughes, Eyvindur Palsson
We prove discrete restriction estimates for a broad class of hypersurfaces and varieties of intermediate codimension. For our result about hypersurfaces, we use Bourgain's arithmet…
Discrete restriction for and related topics
Kevin Hughes, Trevor D. Wooley
Defining the truncated extension operator for a sequence with by putting \[ E{a}(α,β):=\sum_{|n|\leq N}a(n) e(αn^3 + βn), \] we obtain the conjecture…
Bounds for Lacunary maximal functions given by Birch--Magyar averages
Brian Cook, Kevin Hughes
We obtain positive and negative results concerning lacunary discrete maximal operators defined by dilations of sufficiently nonsingular hypersurfaces arising from Diophantine equat…
-improving for discrete spherical averages
Kevin Hughes
We initiate the theory of -improving inequalities for arithmetic averages over hypersurfaces and their maximal functions. In particular, we prove -improving estimat…