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

SN - 0008-4395

VL - 56

SP - 844

EP - 849

JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

IS - 4

ER -