On the distribution of the Euler function of shifted smooth numbers

Stefanie S. Loiperdinger; Igor E. Shparlinski

doi:10.4064/cm120-1-10

On the distribution of the Euler function of shifted smooth numbers

Stefanie S. Loiperdinger^*, Igor E. Shparlinski

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

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

Original language	English
Pages (from-to)	139-148
Number of pages	10
Journal	Colloquium Mathematicum
Volume	120
Issue number	1
DOIs	https://doi.org/10.4064/cm120-1-10
Publication status	Published - 2010

Keywords

Euler function
smooth numbers
LARGE PRIME FACTORS
ARITHMETIC PROGRESSIONS
INTEGERS

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10.4064/cm120-1-10

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title = "On the distribution of the Euler function of shifted smooth numbers",

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",

keywords = "Euler function, smooth numbers, LARGE PRIME FACTORS, ARITHMETIC PROGRESSIONS, INTEGERS",

author = "Loiperdinger, {Stefanie S.} and Shparlinski, {Igor E.}",

year = "2010",

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AU - Loiperdinger, Stefanie S.

AU - Shparlinski, Igor E.

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AB - 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

KW - Euler function

KW - smooth numbers

KW - LARGE PRIME FACTORS

KW - ARITHMETIC PROGRESSIONS

KW - INTEGERS

U2 - 10.4064/cm120-1-10

DO - 10.4064/cm120-1-10

M3 - Article

SN - 0010-1354

VL - 120

SP - 139

EP - 148

JO - Colloquium Mathematicum

JF - Colloquium Mathematicum

IS - 1

ER -

On the distribution of the Euler function of shifted smooth numbers

Abstract

Keywords

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