Geodesic
On fractional parts of rapidly growing functions
Izvestiya. Mathematics, Tome 65 (2001) no. 4, pp. 727-748 
A. A. Karatsuba. On fractional parts of rapidly growing functions. Izvestiya. Mathematics, Tome 65 (2001) no. 4, pp. 727-748. http://geodesic.mathdoc.fr/item/IM2_2001_65_4_a5/
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     author = {A. A. Karatsuba},
     title = {On fractional parts of rapidly growing functions},
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     volume = {65},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2001_65_4_a5/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We study the behaviour of fractional parts of functions $\alpha\exp([\log^c x]\log x)$, where $\alpha$ is a real algebraic number of degree $n\geqslant 2$ and $c$ is an arbitrary positive number less than one.

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