»Ê¹Ú²ÊƱ

Abstract

An affine hypersurface is the set of solutions to a polynomial equation. In this talk, we introduce some new upper and lower bounds for the number of rational points on affine hypersurfaces and with each component of bounded height. This is a relatively new model of point counting with very few results in this direction. Our results rely on a new quantitative version of Hilbert's irreducibility theorem, which is of independent interest.

Ìý