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Proceedings of the American Mathematical Society

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Lattice point problems involving index and joint visibility


Authors: Sneha Chaubey, Albert Tamazyan and Alexandru Zaharescu
Journal: Proc. Amer. Math. Soc. 147 (2019), 3273-3288
MSC (2010): Primary 11P21, 11L07
DOI: https://doi.org/10.1090/proc/14462
Published electronically: March 26, 2019
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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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Additional Information

Sneha Chaubey
Affiliation: Department of Mathematics, IIIT-Delhi, Okhla Industrial Estate-Phase 3, New Delhi-110020, India
Email: sneha@iiitd.ac.in

Albert Tamazyan
Affiliation: Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801
Email: tamazya2@illinois.edu

Alexandru Zaharescu
Affiliation: Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, Illinois 61801; Simion Stoilow Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-014700 Bucharest, Romania
Email: zaharesc@illinois.edu

DOI: https://doi.org/10.1090/proc/14462
Keywords: Visible lattice points, exponential and Kloosterman sums
Received by editor(s): April 25, 2018
Received by editor(s) in revised form: August 9, 2018, and November 6, 2018
Published electronically: March 26, 2019
Communicated by: Amanda Folsom
Article copyright: © Copyright 2019 American Mathematical Society