On the Distribution of the Euler Function of Shifted Smooth Numbers
Stefanie S. Loiperdinger, Igor E. Shparlinski
TL;DR
This paper derives asymptotic formulas for the average values of the Euler function evaluated on shifted smooth numbers, utilizing advanced estimates of their distribution in arithmetic progressions.
Contribution
It introduces new asymptotic formulas for the Euler function on shifted smooth numbers, expanding understanding of their distribution and properties.
Findings
Asymptotic formulas for average Euler function values on shifted smooth numbers.
Utilizes estimates on smooth numbers in arithmetic progressions from Granville, Fouvry, and Tenenbaum.
Provides insights into the distribution of smooth numbers in shifted contexts.
Abstract
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 \'E. Fouvry & G. Tenenbaum.
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Taxonomy
TopicsAnalytic Number Theory Research · Advanced Mathematical Identities · Meromorphic and Entire Functions