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Displaying similar documents to “Multiplicative isometries on the Smirnov class”

Alexander’s projective capacity for polydisks and ellipsoids in ℂ N

Mieczysław Jędrzejowski (1995)

Annales Polonici Mathematici

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Alexander’s projective capacity for the polydisk and the ellipsoid in ℂ N is computed. Sharper versions of two inequalities concerning this capacity and some other capacities in ℂ N are given. A sequence of orthogonal polynomials with respect to an appropriately defined measure supported on a compact subset K in ℂ N is proved to have an asymptotic behaviour in ℂ N similar to that of the Siciak homogeneous extremal function associated with K.

On the Euler function of repdigits

Florian Luca (2008)

Czechoslovak Mathematical Journal

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For a positive integer n we write φ ( n ) for the Euler function of n . In this note, we show that if b > 1 is a fixed positive integer, then the equation φ x b n - 1 b - 1 = y b m - 1 b - 1 , where x , y ∈ { 1 , ... , b - 1 } , has only finitely many positive integer solutions ( x , y , m , n ) .

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.