TY - JOUR
T1 - On the average number of square-free values of polynomials
AU - Shparlinski, Igor E.
PY - 2013/12
Y1 - 2013/12
N2 - We obtain an asymptotic formula for the number of square-free integers in N consecutive values of polynomials on average over integral polynomials of degree at most k and of height at most H, where H ≥ Nk-1+ε for some fixed ε > 0. Individual results of this kind for polynomials of degree k > 3, due to A. Granville (1998), are only known under the ABC-conjecture.
AB - We obtain an asymptotic formula for the number of square-free integers in N consecutive values of polynomials on average over integral polynomials of degree at most k and of height at most H, where H ≥ Nk-1+ε for some fixed ε > 0. Individual results of this kind for polynomials of degree k > 3, due to A. Granville (1998), are only known under the ABC-conjecture.
UR - http://www.scopus.com/inward/record.url?scp=84887534447&partnerID=8YFLogxK
U2 - 10.4153/CMB-2012-021-8
DO - 10.4153/CMB-2012-021-8
M3 - Article
AN - SCOPUS:84887534447
VL - 56
SP - 844
EP - 849
JO - Canadian Mathematical Bulletin
JF - Canadian Mathematical Bulletin
SN - 0008-4395
IS - 4
ER -