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

By

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.

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