Lattice point problems involving index and joint visibility

Chaubey, Sneha; Tamazyan, Albert; Zaharescu, Alexandru

doi:10.1090/proc/14462

Lattice point problems involving index and joint visibility
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by Sneha Chaubey, Albert Tamazyan and Alexandru Zaharescu PDF

Proc. Amer. Math. Soc. 147 (2019), 3273-3288 Request permission

Abstract:

We study questions concerning the distribution of lattice points in dimensions two and higher. We give asymptotic formulas for the number of integer lattice points of fixed index visible from certain admissible sets. We also study the shape of the body $PA_1, \dots , PA_k$ when the lattice points $A_1, \dots , A_k$ move inside a given large ball, and $P$ is a lattice point visible from all $A_i$’s.

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