Displaying similar documents to “Application of uniform asymptotics to the fifth Painlevé transcendent.”

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.