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arXiv · 1601.06867

Irreducible polynomials with several prescribed coefficients

Junsoo Ha
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Abstract

We study the number of irreducible polynomials over $\mathbf{F}_{q}$ 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 $r \leq \left[\left(1/4 - \epsilon\right)n \right]$ for any $\epsilon>0$ and $q$ is large; and when $r\leq\delta n$ for some $\delta>0$ and for any $q$. The result is improved from the earlier work of Pollack that the similar result holds for $r\leq\left[(1-\epsilon)\sqrt{n}\right]$.

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Junsoo Ha. 2016-01-26. Irreducible polynomials with several prescribed coefficients. https://arxiv.org/abs/1601.06867

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