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Proceedings of the American Mathematical Society

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Pinned algebraic distances determined by Cartesian products in $\mathbb {F}_p^2$


Author: Giorgis Petridis
Journal: Proc. Amer. Math. Soc. 145 (2017), 4639-4645
MSC (2010): Primary 11B30
DOI: https://doi.org/10.1090/proc/13649
Published electronically: May 26, 2017
MathSciNet review: 3691983
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Abstract: Let $p$ be an odd prime and $A \subseteq \mathbb {F}_p$ be a subset of the finite field with $p$ elements. We show that $A \times A \subseteq \mathbb {F}_p^2$ determines at least a constant multiple of $\min \{p, |A|^{3/2}\}$ distinct pinned algebraic distances.


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Additional Information

Giorgis Petridis
Affiliation: Department of Mathematics, University of Georgia, Athens, Georgia 30602
MR Author ID: 956366
Email: giorgis@cantab.net

Received by editor(s): October 12, 2016
Received by editor(s) in revised form: December 1, 2016
Published electronically: May 26, 2017
Additional Notes: The author was supported by NSF DMS Grant 1500984
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2017 American Mathematical Society