| Title:
|
Sums of multiplicative function in special arithmetic progressions (English) |
| Author:
|
Feng, Bin |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
69 |
| Issue:
|
1 |
| Year:
|
2019 |
| Pages:
|
1-10 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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). (English) |
| Keyword:
|
Selberg-Delange method |
| Keyword:
|
multiplicative function |
| Keyword:
|
arithmetic progressions |
| MSC:
|
11N37 |
| idZBL:
|
Zbl 07088764 |
| idMR:
|
MR3923569 |
| DOI:
|
10.21136/CMJ.2019.0079-16 |
| . |
| Date available:
|
2019-03-08T14:53:22Z |
| Last updated:
|
2021-04-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147610 |
| . |
| Reference:
|
[1] Cui, Z., Wu, J.: The Selberg-Delange method in short intervals with an application.Acta Arith. 163 (2014), 247-260. Zbl 1303.11108, MR 3206395, 10.4064/aa163-3-4 |
| Reference:
|
[2] Delange, H.: Sur des formules dues à Atle Selberg.Bull. Sci. Math., II. Ser. 83 French (1959), 101-111. Zbl 0106.03305, MR 0113836 |
| Reference:
|
[3] Delange, H.: Sur des formules de Atle Selberg.Acta Arith. 19 French (1971), 105-146. Zbl 0217.31902, MR 0289432, 10.4064/aa-19-2-105-146 |
| Reference:
|
[4] Gallagher, P. X.: Primes in progressions to prime-power modulus.Invent. Math. 16 (1972), 191-201. Zbl 0246.10030, MR 0304327, 10.1007/BF01425492 |
| Reference:
|
[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. Zbl 1195.11129, MR 2392317, 10.1112/plms/pdm029 |
| Reference:
|
[6] Lau, Y.-K.: Summatory formula of the convolution of two arithmetical functions.Monatsh. Math. 136 (2002), 35-45. Zbl 1012.11089, MR 1908079, 10.1007/s006050200032 |
| Reference:
|
[7] Lau, Y.-K., Wu, J.: Sums of some multiplicative functions over a special set of integers.Acta Arith. 101 (2002), 365-394. Zbl 0991.11050, MR 1880049, 10.4064/aa101-4-5 |
| Reference:
|
[8] Pan, C. D., Pan, C. B.: Fundamentals of Analytic Number Theory.Science Press, Beijing (1991), Chinese. MR 2954332 |
| Reference:
|
[9] Selberg, A.: Note on a paper by L. G. Sathe.J. Indian Math. Soc., N. Ser. 18 (1954), 83-87. Zbl 0057.28502, MR 0067143, 10.18311/jims/1954/17018 |
| Reference:
|
[10] Tenenbaum, G.: Introduction to Analytic and Probabilistic Number Theory.Cambridge Studies in Advanced Mathematics 46, Cambridge Univ. Press, Cambridge (1995). Zbl 0831.11001, MR 1342300 |
| Reference:
|
[11] Tenenbaum, G., Wu, J.: Théorie analytique et probabiliste des nombres: 307 exercices corrigés.Belin, Paris (2014), French. MR 1397501 |
| . |
