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October 2019 Distance sets over arbitrary finite fields
Doowon Koh, Sujin Lee, Thang Pham, Chun-Yen Shen
Illinois J. Math. 63(3): 469-484 (October 2019). DOI: 10.1215/00192082-7854872

Abstract

In this paper, we study the Erdős distinct distances problem for Cartesian product sets in the setting of arbitrary finite fields. More precisely, let Fq be an arbitrary finite field and A be a set in Fq. Suppose |A(aG)||G|1/2 for any subfield G and aFq, then |ΔFq(A2)|=|(AA)2+(AA)2||A|1+121. Using the same method, we also obtain some results on sum–product type problems.

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Doowon Koh. Sujin Lee. Thang Pham. Chun-Yen Shen. "Distance sets over arbitrary finite fields." Illinois J. Math. 63 (3) 469 - 484, October 2019. https://doi.org/10.1215/00192082-7854872

Information

Received: 16 January 2019; Revised: 3 May 2019; Published: October 2019
First available in Project Euclid: 19 September 2019

zbMATH: 07110750
MathSciNet: MR4012352
Digital Object Identifier: 10.1215/00192082-7854872

Subjects:
Primary: 11T06
Secondary: 11T60

Rights: Copyright © 2019 University of Illinois at Urbana-Champaign

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Vol.63 • No. 3 • October 2019
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