Type: Article

Asymptotic formulas for certain arithmetic functions

M. Z. Garaev; M. Kühleitner; F. Luca; W. G. Nowak;

Abstract:

This is an extended summary of a talk given by the last named author at the Czecho-Slovake Number Theory Conference 2005, held at Malen-ovice in September 2005. It surveys some recent results concerning asymptotics for a class of arithmetic functions, including, e.g., the second moments of the number-of-divisors function d(n) and of the function r(n) which counts the number of ways to write a positive integer as a sum of two squares. For the proofs, reference is made to original articles by the authors published elsewhere.