International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 1, Pages 1-23

Estimates of convolutions of certain number-theoretic error terms

Aleksandar Ivić

Katedra Matematike RGF-a, Universiteta u Beogradu, Ðušina 7, Beograd 11000, Serbia and Montenegro

Received 13 May 2003

Copyright © 2004 Aleksandar Ivić. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Several estimates for the convolution function C[f(x)]:=1xf(y)f(x/y)(dy/y) and its iterates are obtained when f(x) is a suitable number-theoretic error term. We deal with the case of the asymptotic formula for 0T|ζ(1/2+it)|2kdt(k=1,2), the general Dirichlet divisor problem, the problem of nonisomorphic Abelian groups of given order, and the Rankin-Selberg convolution.