Geodesic
On the Distribution of Irreducible Trinomials
Canadian mathematical bulletin, Tome 54 (2011) no. 4, pp. 748-756

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DOI

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.
DOI : 10.4153/CMB-2011-053-0
Mots-clés : 11L40, 11T06, irreducible trinomials, character sums 
Shparlinski, Igor E. On the Distribution of Irreducible Trinomials. Canadian mathematical bulletin, Tome 54 (2011) no. 4, pp. 748-756. doi: 10.4153/CMB-2011-053-0
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     title = {On the {Distribution} of {Irreducible} {Trinomials}},
     journal = {Canadian mathematical bulletin},
     pages = {748--756},
     year = {2011},
     volume = {54},
     number = {4},
     doi = {10.4153/CMB-2011-053-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-053-0/}
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