On the distribution of the Euler function of shifted smooth numbers
Volume 120 / 2010
Colloquium Mathematicum 120 (2010), 139-148 MSC: 11N25, 11N37. DOI: 10.4064/cm120-1-10
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.