Sum-product estimates and multiplicative orders of γ and γ+γ -1 in finite fields

Igor Shparlinski

doi:10.1017/S0004972711002887

Sum-product estimates and multiplicative orders of γ and γ+γ ^-1 in finite fields

Igor Shparlinski^*

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Using a recent result on the sum-product problem, we estimate the number of elements γ in a prime finite field such that both γ and γ+γ ^-1 are of small order.

Original language	English
Pages (from-to)	505-508
Number of pages	4
Journal	Bulletin of the Australian Mathematical Society
Volume	85
Issue number	3
DOIs	https://doi.org/10.1017/S0004972711002887 https://doi.org/10.1017/S0004972712001062
Publication status	Published - Jun 2012

Bibliographical note

Corrigendum can be found in Bulletin of the Australian Mathematical Society, 87(3), pp. 527-528, 2013.
https://doi.org/10.1017/S0004972712001062

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title = "Sum-product estimates and multiplicative orders of γ and γ+γ -1 in finite fields",

abstract = "Using a recent result on the sum-product problem, we estimate the number of elements γ in a prime finite field such that both γ and γ+γ -1 are of small order.",

author = "Igor Shparlinski",

note = "Corrigendum can be found in Bulletin of the Australian Mathematical Society, 87(3), pp. 527-528, 2013. https://doi.org/10.1017/S0004972712001062",

year = "2012",

month = jun,

doi = "10.1017/S0004972711002887",

language = "English",

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pages = "505--508",

journal = "Bulletin of the Australian Mathematical Society",

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T1 - Sum-product estimates and multiplicative orders of γ and γ+γ -1 in finite fields

AU - Shparlinski, Igor

N1 - Corrigendum can be found in Bulletin of the Australian Mathematical Society, 87(3), pp. 527-528, 2013. https://doi.org/10.1017/S0004972712001062

PY - 2012/6

Y1 - 2012/6

N2 - Using a recent result on the sum-product problem, we estimate the number of elements γ in a prime finite field such that both γ and γ+γ -1 are of small order.

AB - Using a recent result on the sum-product problem, we estimate the number of elements γ in a prime finite field such that both γ and γ+γ -1 are of small order.

UR - https://www.scopus.com/pages/publications/84860797129

U2 - 10.1017/S0004972711002887

DO - 10.1017/S0004972711002887

M3 - Article

AN - SCOPUS:84860797129

SN - 0004-9727

VL - 85

SP - 505

EP - 508

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

IS - 3

ER -

Sum-product estimates and multiplicative orders of γ and γ+γ ^-1 in finite fields

Abstract

Bibliographical note

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