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On the Distribution of Irreducible Trinomials |
Canad. Math. Bull. 54(2011), 748-756
Published:2011-03-24
Printed: Dec 2011
Printed: Dec 2011
- Igor E. Shparlinski,
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.
| Keywords: | irreducible trinomials, character sums |
| MSC Classifications: |
11L40 - Estimates on character sums 11T06 - Polynomials |