On the distribution of irreducible trinomials

Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We obtain new results about the number of trinomials t n + at + b with integer coefficients in a box (a, b) ∈ [C,C + A] × [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.

Original languageEnglish
Pages (from-to)748-756
Number of pages9
JournalCanadian Mathematical Bulletin
Issue number4
Publication statusPublished - Dec 2011


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