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arXiv · 2103.10889

$p$-adic Directions of Primitive Vectors

Antonin Guilloux·Tal Horesh
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Abstract

Linnik type problems concern the distribution of projections of integral points on the unit sphere as their norm increases, and different generalizations of this phenomenon. Our work addresses a question of this type: we prove the uniform distribution of the projections of primitive $\mathbb{Z}^{2}$ points in the $p$-adic unit sphere, as their (real) norm tends to infinity. The proof is via counting lattice points in semi-simple $S$-arithmetic groups.

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Antonin Guilloux, Tal Horesh. 2021-03-19. $p$-adic Directions of Primitive Vectors. https://arxiv.org/abs/2103.10889

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