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Banks and Shparlinski, “Congruences and exponential sums with the sum of aliquot divisors function”, International journal of Number Theory, 2008.

has been cited by the following article:

Article

Mean Values of Arithmetic Functions under Congruences with the Euler Function

1Montanuniversität Leoben Department Mathematik und Informationstechnologie, Austria

2Department of Mathematics, Faculty of Sciences of Monastir, Tunisia


Turkish Journal of Analysis and Number Theory. 2020, Vol. 8 No. 2, 39-48
DOI: 10.12691/tjant-8-2-4
Copyright © 2020 Science and Education Publishing

Cite this paper:
Myriam Amri, Khadija Mbarki. Mean Values of Arithmetic Functions under Congruences with the Euler Function. Turkish Journal of Analysis and Number Theory. 2020; 8(2):39-48. doi: 10.12691/tjant-8-2-4.

Correspondence to: Myriam  Amri, Montanuniversität Leoben Department Mathematik und Informationstechnologie, Austria. Email: myriam.amri@unileoben.ac.at

Abstract

We examine the average order of some arithmetic functions written as sums over Euler function in arithmetic progression and in general over such that is a prime number, an integer and is a polynomial function with integer coefficients and a degree that is not constant modulo Our results are based on various estimates of rational exponential sums with the Euler Function in arithmetic progression which are due to William Banks and Igor E. Shparlinski.

Keywords