Geodesic
On the sum of the first $n$ values of the Euler function
R. Balasubramanian1 ; Florian Luca2 ; Dimbinaina Ralaivaosaona3
1 The Institute of Mathematical Sciences Chennai 600 113, India
2 Mathematical Institute UNAM Juriquilla 76230 Santiago de Querétaro, México and School of Mathematics University of the Witwatersrand P.O. Box Wits 2050 Johannesburg, South Africa
3 African Institute for Mathematical Sciences 6 Melrose Ave. Muizenberg, South Africa
Acta Arithmetica, Tome 163 (2014) no. 3, pp. 199-201.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $\phi (n)$ be the Euler function of $n$. We put $E(n)= \sum _{m\le n} \phi (m)-(3/\pi ^2) n^2$ and give an asymptotic formula for the second moment of $E(n)$.
DOI : 10.4064/aa163-3-1
Keywords: phi euler function put sum phi asymptotic formula second moment

R. Balasubramanian 1 ; Florian Luca 2 ; Dimbinaina Ralaivaosaona 3

1 The Institute of Mathematical Sciences Chennai 600 113, India
2 Mathematical Institute UNAM Juriquilla 76230 Santiago de Querétaro, México and School of Mathematics University of the Witwatersrand P.O. Box Wits 2050 Johannesburg, South Africa
3 African Institute for Mathematical Sciences 6 Melrose Ave. Muizenberg, South Africa 
@article{10_4064_aa163_3_1,
     author = {R. Balasubramanian and Florian Luca and Dimbinaina Ralaivaosaona},
     title = {On the sum of the first $n$ values of the {Euler} function},
     journal = {Acta Arithmetica},
     pages = {199--201},
     publisher = {mathdoc},
     volume = {163},
     number = {3},
     year = {2014},
     doi = {10.4064/aa163-3-1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/aa163-3-1/}
}
TY  - JOUR
AU  - R. Balasubramanian
AU  - Florian Luca
AU  - Dimbinaina Ralaivaosaona
TI  - On the sum of the first $n$ values of the Euler function
JO  - Acta Arithmetica
PY  - 2014
SP  - 199
EP  - 201
VL  - 163
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/aa163-3-1/
DO  - 10.4064/aa163-3-1
LA  - en
ID  - 10_4064_aa163_3_1
ER  - 
%0 Journal Article
%A R. Balasubramanian
%A Florian Luca
%A Dimbinaina Ralaivaosaona
%T On the sum of the first $n$ values of the Euler function
%J Acta Arithmetica
%D 2014
%P 199-201
%V 163
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/aa163-3-1/
%R 10.4064/aa163-3-1
%G en
%F 10_4064_aa163_3_1
R. Balasubramanian; Florian Luca; Dimbinaina Ralaivaosaona. On the sum of the first $n$ values of the Euler function. Acta Arithmetica, Tome 163 (2014) no. 3, pp. 199-201. doi : 10.4064/aa163-3-1. http://geodesic.mathdoc.fr/articles/10.4064/aa163-3-1/

Cité par Sources :