On the average number of square-free values of polynomials

Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)844-849
Number of pages6
JournalCanadian Mathematical Bulletin
Issue number4
Publication statusPublished - Dec 2013


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