### 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 PA1, . . . ,PA_{k} when the lattice points A1, . . . , A_{k} move inside a given large ball, and P is a lattice point visible from all Ai's.

Original language | English (US) |
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Pages (from-to) | 3273-3288 |

Number of pages | 16 |

Journal | Proceedings of the American Mathematical Society |

Volume | 147 |

Issue number | 8 |

DOIs | |

State | Published - Mar 26 2019 |

### Keywords

- Exponential And Kloosterman Sums
- Visible Lattice Points

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Chaubey, S., Tamazyan, A., & Zaharescu, A. (2019). Lattice point problems involving index and joint visibility.

*Proceedings of the American Mathematical Society*,*147*(8), 3273-3288. https://doi.org/10.1090/proc/14462