Subcritical paucity and ${\ell }^p$-improving estimates for finite-type polynomial curves

Abstract

I prove new subcritical bounds for the ${\ell }^p$-improving problem along restricted subsets of a degenerate curve. The key input is a new paucity estimate for associated inhomogeneous equations which is proven using an elimination method due to Wooley and Parsell--Wooley.

12 pages. Comments welcome!