Density of rational points near/on compact manifolds with certain curvature conditions

Abstract: In this talk I will discuss joint work with Shuntaro Yamagishi where we establish an asymptotic formula for the number of rational points, with bounded denominators, within a given distance to a compact submanifold M of R^n with a certain curvature condition. Technically we build on work of Huang on the density of rational points near hypersurfaces. One of our goals is to explore generalisations to higher codimension. In particular we show that assuming certain curvature conditions in codimension at least two, leads to upper bounds for the number of rational points on M which are even stronger than what would be predicted by the analogue of Serre's dimension growth conjecture.

number theory

Audience: researchers in the topic

Number theory by the sea

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