Displaying similar documents to “Alexander’s projective capacity for polydisks and ellipsoids in N

The homogeneous transfinite diameter of a compact subset of N

Mieczysław Jędrzejowski (1991)

Annales Polonici Mathematici

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Let K be a compact subset of N . A sequence of nonnegative numbers defined by means of extremal points of K with respect to homogeneous polynomials is proved to be convergent. Its limit is called the homogeneous transfinite diameter of K. A few properties of this diameter are given and its value for some compact subsets of N is computed.

An asymptotic expansion.

Mincu, Gabriel (2003)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

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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 ) .