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On the distribution of the Euler function of shifted smooth numbers

Stefanie S. Loiperdinger; Igor E. Shparlinski — 2010

Colloquium Mathematicae

We give asymptotic formulas for some average values of the Euler function on shifted smooth numbers. The result is based on various estimates on the distribution of smooth numbers in arithmetic progressions which are due to A. Granville and É. Fouvry & G. Tenenbaum.

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