Displaying similar documents to “Absolutely continuous distribution functions of additive functions f ( p ) = ( l o g p ) - a , a > 0 ”

On the value distribution of a class of arithmetic functions

Werner Georg Nowak (1996)

Commentationes Mathematicae Universitatis Carolinae

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This article deals with the value distribution of multiplicative prime-independent arithmetic functions ( α ( n ) ) with α ( n ) = 1 if n is N -free ( N ≥ 2 a fixed integer), α ( n ) > 1 else, and α ( 2 n ) → ∞ . An asymptotic result is established with an error term probably definitive on the basis of the present knowledge about the zeros of the zeta-function. Applications to the enumerative functions of Abelian groups and of semisimple rings of given finite order are discussed.

Additive properties of dense subsets of sifted sequences

Olivier Ramaré, Imre Z. Ruzsa (2001)

Journal de théorie des nombres de Bordeaux

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We examine additive properties of dense subsets of sifted sequences, and in particular prove under very general assumptions that such a sequence is an additive asymptotic basis whose order is very well controlled.