Polynomial values in subfields and affine subspaces of finite fields

Oliver Roche-Newton; Igor E. Shparlinski

doi:10.1093/qmath/hau032

Polynomial values in subfields and affine subspaces of finite fields

Oliver Roche-Newton, Igor E. Shparlinski^*

^*Corresponding author for this work

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

7 Citations (Scopus)

Abstract

For an integer r, a prime power q and a polynomial f over a finite field F_q ^r of q^r elements, we obtain an upper bound on the frequency of elements in an orbit generated by iterations of f which fall in a proper subfield of F_q ^r . We also obtain similar results for elements in affine subspaces of F_q ^r , considered as a linear space over F_q.

Original language	English
Pages (from-to)	693-706
Number of pages	14
Journal	Quarterly Journal of Mathematics
Volume	66
Issue number	2
DOIs	https://doi.org/10.1093/qmath/hau032
Publication status	Published - 2015
Externally published	Yes

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10.1093/qmath/hau032

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title = "Polynomial values in subfields and affine subspaces of finite fields",

abstract = "For an integer r, a prime power q and a polynomial f over a finite field Fq r of qr elements, we obtain an upper bound on the frequency of elements in an orbit generated by iterations of f which fall in a proper subfield of Fq r . We also obtain similar results for elements in affine subspaces of Fq r , considered as a linear space over Fq.",

author = "Oliver Roche-Newton and Shparlinski, {Igor E.}",

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AU - Roche-Newton, Oliver

AU - Shparlinski, Igor E.

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Y1 - 2015

N2 - For an integer r, a prime power q and a polynomial f over a finite field Fq r of qr elements, we obtain an upper bound on the frequency of elements in an orbit generated by iterations of f which fall in a proper subfield of Fq r . We also obtain similar results for elements in affine subspaces of Fq r , considered as a linear space over Fq.

AB - For an integer r, a prime power q and a polynomial f over a finite field Fq r of qr elements, we obtain an upper bound on the frequency of elements in an orbit generated by iterations of f which fall in a proper subfield of Fq r . We also obtain similar results for elements in affine subspaces of Fq r , considered as a linear space over Fq.

UR - http://www.scopus.com/inward/record.url?scp=84930702535&partnerID=8YFLogxK

UR - http://purl.org/au-research/grants/arc/DP130100237

UR - http://purl.org/au-research/grants/arc/DP140100118

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DO - 10.1093/qmath/hau032

M3 - Article

AN - SCOPUS:84930702535

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JO - Quarterly Journal of Mathematics

JF - Quarterly Journal of Mathematics

IS - 2

ER -

Polynomial values in subfields and affine subspaces of finite fields

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New Applications of Additive Combinatorics in Number Theory and Graph Theory

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Polynomial values in subfields and affine subspaces of finite fields

Abstract

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New Applications of Additive Combinatorics in Number Theory and Graph Theory

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