2015/11/06 by R. Balasubramanian, Balasubramanian, R., Sumit Giri +3
Mathematics · #11N37 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11N37
paper · pdf · doi:10.48550/arxiv.1511.02221
13 pages
arxiv created 2016/09/27 · arxiv updated 2016/09/28
In this paper, we study sums of shifted products ∑n ≤ x F(n) G(n-h) for any |h| ≤ x/2 and arithmetic functions F=f*1 and G=g*1, with f and g small. We obtain asymptotic formula for different orders of magnitude of f and g. We also provide asymptotic formula for sums of the type ∑n ≤ x μ2(n) G(n-h), where G=g*1 and g is small. For small order of magnitudes of f and g, we improve the error terms and make them independent of h.