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On the Distribution of Irreducible Trinomials
Published online by Cambridge University Press: 20 November 2018
Abstract
We obtain new results about the number of trinomials ${{t}^{n}}\,+\,at\,+\,b$ with integer coefficients in a box $(a,\,b)\,\in \,[C,\,C\,+\,A]\,\times \,[D,\,D\,+\,B]$ that are irreducible modulo a prime $p$. As a by-product we show that for any $p$ there are irreducible polynomials of height at most ${{p}^{1/2+o(1)}}$, improving on the previous estimate of ${{p}^{2/3+o(1)}}$ obtained by the author in 1989.
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- Copyright © Canadian Mathematical Society 2011
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