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ON SUM OF PRODUCTS AND THE ERDŐS DISTANCE PROBLEM OVER FINITE FIELDS

Part of: Sequences and sets

Published online by Cambridge University Press:  21 June 2011

LE ANH VINH
LE ANH VINH*
Affiliation:
Mathematics Department, Harvard University, Cambridge, MA, 20138, USA (email: [email protected])
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Abstract

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For a prime power q, let 𝔽q be the finite field of q elements. We show that 𝔽*q⊆d𝒜2 for almost every subset 𝒜⊂𝔽q of cardinality ∣𝒜∣≫q1/d. Furthermore, if q=p is a prime, and 𝒜⊆𝔽p of cardinality ∣𝒜∣≫p1/2(log p)1/d, then d𝒜2 contains both large and small residues. We also obtain some results of this type for the Erdős distance problem over finite fields.

Keywords

sum of productsErdős distance problem

MSC classification

Secondary: 11B75: Other combinatorial number theory
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 1 , August 2011 , pp. 1 - 9
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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