GIOVANNI COPPOLA

On the symmetry of square-free numbers in almost all short intervals


Pages: 205-212
Received: 23 February 2004   
Mathematics Subject Classification (2000): 11N25 - 11N36 - 11N37

Abstract: In this paper we study the symmetry of the square-free numbers in almost all short intervals; by elementary methods (based on the Large Sieve) we give an upper bound for the mean-square (over the interval N < x ≤2N) of the "symmetry sum" ∑ _{|n-x| ≤ h} sgn (n-x) μ^|2(n) (sgn (t): = t/ |t|, sgn (0)=0).