Article ID Journal Published Year Pages File Type
4582666 Finite Fields and Their Applications 2016 16 Pages PDF
Abstract

We study the number of irreducible polynomials over FqFq with some coefficients prescribed. Using the technique developed by Bourgain, we show that there is an irreducible polynomial of degree n with r   coefficients prescribed in any location when r≤[(1/4−ϵ)n]r≤[(1/4−ϵ)n] for any ϵ>0ϵ>0 and q   is large; and when r≤δnr≤δn for some δ>0δ>0 and for any q  . The result improves earlier work of Pollack stating that a similar result holds for r≤[(1−ϵ)n].

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Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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