Mean Values of Arithmetic Functions under Congruences with the Euler Function.

Myriam Amri; Khadija Mbarki

doi:10.12691/tjant-8-2-4

Mean Values of Arithmetic Functions under Congruences with the Euler Function.

Myriam Amri, Khadija Mbarki

Chair of Mathematics, Statistics and Geometry (380)

Faculty of Sciences of Monastir

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

Abstract

We consider examining the average order of some arithmetic functions written as sums over divisors d of n satisfying ϕ(d) ≡ a mod p and
f(ϕ(d)) ≡ a mod p such that p is a prime number that is coprime with the
integer a and f is a polynomial function with integer coefficients and a degree
d ≥ 2 that is not constant modulo p.

Original language	English
Pages (from-to)	39-48
Number of pages	10
Journal	Turkish Journal of Analysis and Number Theory
Volume	8.2020
Issue number	2
DOIs	https://doi.org/10.12691/tjant-8-2-4
Publication status	Published - 13 Jul 2020

Keywords

11A63, 11L03, 11N05.

Access to Document

10.12691/tjant-8-2-4Licence: CC BY

Cite this

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title = "Mean Values of Arithmetic Functions under Congruences with the Euler Function.",

abstract = "We consider examining the average order of some arithmetic functions written as sums over divisors d of n satisfying ϕ(d) ≡ a mod p andf(ϕ(d)) ≡ a mod p such that p is a prime number that is coprime with theinteger a and f is a polynomial function with integer coefficients and a degreed ≥ 2 that is not constant modulo p.",

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AB - We consider examining the average order of some arithmetic functions written as sums over divisors d of n satisfying ϕ(d) ≡ a mod p andf(ϕ(d)) ≡ a mod p such that p is a prime number that is coprime with theinteger a and f is a polynomial function with integer coefficients and a degreed ≥ 2 that is not constant modulo p.

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JO - Turkish Journal of Analysis and Number Theory

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