Analytic number theory, Proc. Conf., Temple Univ./Phila. 1980, Lect. Notes Math. 899, 197-220 (1981).
[For the entire collection see Zbl 0465.00008.]
This paper establishes the following interesting and deep results about the arithmetic function , defined by , i.e. is the arithmetic mean of the divisors of : If denotes the number of integers with and not an integer, then
Another teorem, in connection with (1), is the following: Denote for every positive real number the number by . Then for any between 0 and 2, the set of integers for which has asymptotic density 1, the set of for which has asymptotic density 0, and the set of for which has asymptotic desity . The proofs are long and complicated, with applications of results from various parts of number theory. To mention only a few: sieve methods, the generalized Erdős-Kac theorem and Tauberian theorems of Delange.