Counting Rational Points In Non-Isotropic Neighborhoods of Manifolds
Counting Rational Points In Non-Isotropic Neighborhoods of Manifolds
In this manuscript, we initiate the study of the number of rational points with bounded denominators, contained in a non-isotropic $\delta_1\times\ldots\times \delta_R$ neighborhood of a compact submanifold $\mathcal{M}$ of codimension $R$ in $\mathbb{R}^{M}$. We establish an upper bound for this counting function which holds when $\mathcal{M}$ satisfies a strong curvature …