Sankhya: The Indian Journal of Statistics
1995, Volume 57, Series A, Pt. 1, pp. 29--32
ABSOLUTE CONTINUITY OF THE DISTRIBUTIONS OF ADDITIVE ARITHMATIC FUNCTIONS
GUTTI JOGESH BABU, Pennsylvania State University
SUMMARY. It is well known that the distribution of a real valued additive arithmetic function f, if it exists, is either purely discrete, purely continuous singular, or purely absolutely continuous. In this paper the distribution of f is shown to be absolutely continuous, if f(p) does not approach zero "too fast", as $p \rightarrow \infty$ through primes.
AMS (1980) subject classification. Primary 11N60, 11K65; secondary 60E10; 11N64.
Key words and phrases. Singular distribution, characteristic function, Plancherel theorem.
This article in mathematical reviews.