The analog of the Erdös distance problem in finite fields-Reference-Cited by-同舟云学术

The analog of the Erdös distance problem in finite fields

Published:2017-09-20 Issue:09 Volume:13 Page:2319-2333
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Adhikari S. D.¹,Mukhopadhyay Anirban²^ORCID,Ram Murty M.³

Affiliation:

1. Harish-Chandra Research Institute, HBNI, Chhatnag Road, Jhusi, Allahabad 211 019, India

2. Institute of Mathematical Sciences, HBNI, CIT Campus, Taramani, Chennai 600113, India

3. Department of Mathematics and Statistics, Jeffery Hall, Queen’s University, Kingston, Ontario, Canada K7L 3N6, Canada

Abstract

In this paper, we give a proof of the result of Iosevich and Rudnev [Erdös distance problem in vector spaces over finite fields, Trans. Amer. Math. Soc. 359 (2007) 6127–6142] on the analog of the Erdös–Falconer distance problem in the case of a finite field of characteristic [Formula: see text], where [Formula: see text] is an odd prime, without using estimates for Kloosterman sums. We also address the case of characteristic 2.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042117501275

Reference7 articles.

1. Group actions and geometric combinatorics in 𝔽 q d $\mathbb{F}_{q}^{d}$

2. The Erdös–Falconer Distance Problem, Exponential Sums, and Fourier Analytic Approach to Incidence Theorems in Vector Spaces over Finite Fields

3. Erdös distance problem in vector spaces over finite fields

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