Geodesic
Sums of multiplicative function in special arithmetic progressions
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 1-10 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We find, via the Selberg-Delange method, an asymptotic formula for the mean of arithmetic functions on certain APs. It generalizes a result due to Cui and Wu (2014).
We find, via the Selberg-Delange method, an asymptotic formula for the mean of arithmetic functions on certain APs. It generalizes a result due to Cui and Wu (2014).
DOI : 10.21136/CMJ.2019.0079-16
Classification : 11N37
Keywords: Selberg-Delange method; multiplicative function; arithmetic progressions 
@article{10_21136_CMJ_2019_0079_16,
     author = {Feng, Bin},
     title = {Sums of multiplicative function in special arithmetic progressions},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1--10},
     year = {2019},
     volume = {69},
     number = {1},
     doi = {10.21136/CMJ.2019.0079-16},
     mrnumber = {3923569},
     zbl = {07088764},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2019.0079-16/}
}
TY  - JOUR
AU  - Feng, Bin
TI  - Sums of multiplicative function in special arithmetic progressions
JO  - Czechoslovak Mathematical Journal
PY  - 2019
SP  - 1
EP  - 10
VL  - 69
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2019.0079-16/
DO  - 10.21136/CMJ.2019.0079-16
LA  - en
ID  - 10_21136_CMJ_2019_0079_16
ER  - 
%0 Journal Article
%A Feng, Bin
%T Sums of multiplicative function in special arithmetic progressions
%J Czechoslovak Mathematical Journal
%D 2019
%P 1-10
%V 69
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2019.0079-16/
%R 10.21136/CMJ.2019.0079-16
%G en
%F 10_21136_CMJ_2019_0079_16
Feng, Bin. Sums of multiplicative function in special arithmetic progressions. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 1-10. doi: 10.21136/CMJ.2019.0079-16

[1] Cui, Z., Wu, J.: The Selberg-Delange method in short intervals with an application. Acta Arith. 163 (2014), 247-260. | DOI | MR | JFM

[2] Delange, H.: Sur des formules dues à Atle Selberg. Bull. Sci. Math., II. Ser. 83 French (1959), 101-111. | MR | JFM

[3] Delange, H.: Sur des formules de Atle Selberg. Acta Arith. 19 French (1971), 105-146. | DOI | MR | JFM

[4] Gallagher, P. X.: Primes in progressions to prime-power modulus. Invent. Math. 16 (1972), 191-201. | DOI | MR | JFM

[5] Hanrot, G., Tenenbaum, G., Wu, J.: Averages of certain multiplicative functions over friable integers. II. Proc. Lond. Math. Soc. (3) 96 French (2008), 107-135. | DOI | MR | JFM

[6] Lau, Y.-K.: Summatory formula of the convolution of two arithmetical functions. Monatsh. Math. 136 (2002), 35-45. | DOI | MR | JFM

[7] Lau, Y.-K., Wu, J.: Sums of some multiplicative functions over a special set of integers. Acta Arith. 101 (2002), 365-394. | DOI | MR | JFM

[8] Pan, C. D., Pan, C. B.: Fundamentals of Analytic Number Theory. Science Press, Beijing (1991), Chinese. | MR

[9] Selberg, A.: Note on a paper by L. G. Sathe. J. Indian Math. Soc., N. Ser. 18 (1954), 83-87. | DOI | MR | JFM

[10] Tenenbaum, G.: Introduction to Analytic and Probabilistic Number Theory. Cambridge Studies in Advanced Mathematics 46, Cambridge Univ. Press, Cambridge (1995). | MR | JFM

[11] Tenenbaum, G., Wu, J.: Théorie analytique et probabiliste des nombres: 307 exercices corrigés. Belin, Paris (2014), French. | MR

Cité par Sources :