### Weighted composition operators on growth spaces.

Dubtsov, E.S. (2009)

Sibirskij Matematicheskij Zhurnal

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Dubtsov, E.S. (2009)

Sibirskij Matematicheskij Zhurnal

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Acta Arithmetica

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Jakimczuk, Rafael (2010)

Journal of Integer Sequences [electronic only]

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Bulletin. Classe des Sciences Mathématiques et Naturelles. Sciences Mathématiques

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M. Nedeljkov, S. Pilipović (2002)

Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques

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Lau, Yuk-Kam, Tsang, Kai-Man (2008)

Annales Academiae Scientiarum Fennicae. Mathematica

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Tomás Hobza, Igor Vajda (2001)

Revista Matemática Complutense

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We consider positive real valued random data X with the decadic representation X = Σ D 10 and the first significant digit D = D(X) in {1,2,...,9} of X defined by the condition D = D ≥ 1, D = D = ... = 0. The data X are said to satisfy the Newcomb-Benford law if P{D=d} = log(d+1 / d) for all d in {1,2,...,9}. This law holds for example for the data with logX uniformly distributed on an interval (m,n) where m and n are integers. We show that if logX has a distribution...

Harald A. Helfgott (2007)

Journal de Théorie des Nombres de Bordeaux

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Let $f\in \mathbb{Z}\left[x\right]$ be a polynomial of degree $d\ge 3$ without roots of multiplicity $d$ or $(d-1)$. Erdős conjectured that, if $f$ satisfies the necessary local conditions, then $f\left(p\right)$ is free of $(d-1)$th powers for infinitely many primes $p$. This is proved here for all $f$ with sufficiently high entropy. The proof serves to demonstrate two innovations: a strong repulsion principle for integer points on curves of positive genus, and a number-theoretical analogue of Sanov’s theorem from the theory of large deviations. ...

Stojan Radenović, Mirjana Pavlović (2003)

Kragujevac Journal of Mathematics

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