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On the Distribution of Irreducible Trinomials

Published online by Cambridge University Press:  20 November 2018

Igor E. Shparlinski
Igor E. Shparlinski*
Affiliation:
Department of Computing, Macquarie University, Sydney, NSW 2109, Australiae-mail: [email protected]
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Abstract

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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.

Keywords

11L4011T06irreducible trinomialscharacter sums
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 4 , 01 December 2011 , pp. 748 - 756
Copyright
Copyright © Canadian Mathematical Society 2011

References

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