In his paper [14], A. Granville proved several strong results about the distribution of square-free values of polynomials, under the assumption of the abc-conjecture. In our thesis, we generalize...Show moreIn his paper [14], A. Granville proved several strong results about the distribution of square-free values of polynomials, under the assumption of the abc-conjecture. In our thesis, we generalize some of Granville’s results to k-free values of polynomials (i.e., values of polynomials not divisible by the k-th power of a prime) . Further, we generalize a result of Granville on the gaps between consecutive square-free numbers to gaps between integers, such that the values of a given polynomial f evaluated at them are k-free. All our results are under assumption of the abc-conjecture.Show less
