TY - JOUR
T1 - On the distribution of irreducible trinomials
AU - Shparlinski, Igor E.
PY - 2011/12
Y1 - 2011/12
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84865684386&partnerID=8YFLogxK
U2 - 10.4153/CMB-2011-053-0
DO - 10.4153/CMB-2011-053-0
M3 - Article
AN - SCOPUS:84865684386
SN - 0008-4395
VL - 54
SP - 748
EP - 756
JO - Canadian Mathematical Bulletin
JF - Canadian Mathematical Bulletin
IS - 4
ER -