Journal Article

POLYNOMIAL VALUES IN SUBFIELDS AND AFFINE SUBSPACES OF FINITE FIELDS

Oliver Roche-Newton and Igor E. Shparlinski

in The Quarterly Journal of Mathematics

Volume 66, issue 2, pages 693-706
Published in print June 2015 | ISSN: 0033-5606
Published online December 2014 | e-ISSN: 1464-3847 | DOI: https://dx.doi.org/10.1093/qmath/hau032
POLYNOMIAL VALUES IN SUBFIELDS AND AFFINE SUBSPACES OF FINITE FIELDS

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

Journal Article.  4859 words. 

Subjects: Pure Mathematics

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