On additive properties of product sets in an arbitrary finite field

A Glibichuk; M Rudnev

doi:10.1007/s11854-009-0021-4

On additive properties of product sets in an arbitrary finite field

A Glibichuk
, M Rudnev

Research output: Contribution to journal › Article (Academic Journal) › peer-review

14 Citations (Scopus)

Abstract

It is proved that for any two subsets A and B of an arbitrary finite field $ \mathbb{F}_q $Fqsuch that |A||B| > q, the identity 10AB = $ \mathbb{F}_q $Fqholds. Under the assumption |A||B| ⩾2q, this improves to 8AB = $ \mathbb{F}_q $Fq.

Translated title of the contribution	On additive properties of product sets in an arbitrary finite field
Original language	English
Pages (from-to)	159 - 170
Number of pages	12
Journal	Journal d'Analyse Mathématique
Volume	108
Issue number	1
DOIs	https://doi.org/10.1007/s11854-009-0021-4
Publication status	Published - May 2009

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Publisher: Springer

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10.1007/s11854-009-0021-4

http://link.springer.com/article/10.1007%2Fs11854-009-0021-4

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title = "On additive properties of product sets in an arbitrary finite field",

abstract = "It is proved that for any two subsets A and B of an arbitrary finite field \$ \textbackslash{}mathbb\{F\}\_q \$Fqsuch that |A||B| > q, the identity 10AB = \$ \textbackslash{}mathbb\{F\}\_q \$Fqholds. Under the assumption |A||B| ⩾2q, this improves to 8AB = \$ \textbackslash{}mathbb\{F\}\_q \$Fq.",

author = "A Glibichuk and M Rudnev",

note = "Publisher: Springer",

year = "2009",

month = may,

doi = "10.1007/s11854-009-0021-4",

language = "English",

volume = "108",

pages = "159 -- 170",

journal = "Journal d'Analyse Math{\'e}matique",

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T1 - On additive properties of product sets in an arbitrary finite field

AU - Glibichuk, A

AU - Rudnev, M

N1 - Publisher: Springer

PY - 2009/5

Y1 - 2009/5

N2 - It is proved that for any two subsets A and B of an arbitrary finite field $ \mathbb{F}_q $Fqsuch that |A||B| > q, the identity 10AB = $ \mathbb{F}_q $Fqholds. Under the assumption |A||B| ⩾2q, this improves to 8AB = $ \mathbb{F}_q $Fq.

AB - It is proved that for any two subsets A and B of an arbitrary finite field $ \mathbb{F}_q $Fqsuch that |A||B| > q, the identity 10AB = $ \mathbb{F}_q $Fqholds. Under the assumption |A||B| ⩾2q, this improves to 8AB = $ \mathbb{F}_q $Fq.

U2 - 10.1007/s11854-009-0021-4

DO - 10.1007/s11854-009-0021-4

M3 - Article (Academic Journal)

SN - 0021-7670

VL - 108

SP - 159

EP - 170

JO - Journal d'Analyse Mathématique

JF - Journal d'Analyse Mathématique

IS - 1

ER -

On additive properties of product sets in an arbitrary finite field

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