Sums of multiplicative function in special arithmetic progressions

Bin Feng

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 1, page 1-10
  • ISSN: 0011-4642

Abstract

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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).

How to cite

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Feng, Bin. "Sums of multiplicative function in special arithmetic progressions." Czechoslovak Mathematical Journal 69.1 (2019): 1-10. <http://eudml.org/doc/294844>.

@article{Feng2019,
abstract = {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).},
author = {Feng, Bin},
journal = {Czechoslovak Mathematical Journal},
keywords = {Selberg-Delange method; multiplicative function; arithmetic progressions},
language = {eng},
number = {1},
pages = {1-10},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Sums of multiplicative function in special arithmetic progressions},
url = {http://eudml.org/doc/294844},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Feng, Bin
TI - Sums of multiplicative function in special arithmetic progressions
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 1
SP - 1
EP - 10
AB - 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).
LA - eng
KW - Selberg-Delange method; multiplicative function; arithmetic progressions
UR - http://eudml.org/doc/294844
ER -

References

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  1. Cui, Z., Wu, J., 10.4064/aa163-3-4, Acta Arith. 163 (2014), 247-260. (2014) Zbl1303.11108MR3206395DOI10.4064/aa163-3-4
  2. Delange, H., Sur des formules dues à Atle Selberg, Bull. Sci. Math., II. Ser. 83 French (1959), 101-111. (1959) Zbl0106.03305MR0113836
  3. Delange, H., 10.4064/aa-19-2-105-146, Acta Arith. 19 French (1971), 105-146. (1971) Zbl0217.31902MR0289432DOI10.4064/aa-19-2-105-146
  4. Gallagher, P. X., 10.1007/BF01425492, Invent. Math. 16 (1972), 191-201. (1972) Zbl0246.10030MR0304327DOI10.1007/BF01425492
  5. Hanrot, G., Tenenbaum, G., Wu, J., 10.1112/plms/pdm029, Proc. Lond. Math. Soc. (3) 96 French (2008), 107-135. (2008) Zbl1195.11129MR2392317DOI10.1112/plms/pdm029
  6. Lau, Y.-K., 10.1007/s006050200032, Monatsh. Math. 136 (2002), 35-45. (2002) Zbl1012.11089MR1908079DOI10.1007/s006050200032
  7. Lau, Y.-K., Wu, J., 10.4064/aa101-4-5, Acta Arith. 101 (2002), 365-394. (2002) Zbl0991.11050MR1880049DOI10.4064/aa101-4-5
  8. Pan, C. D., Pan, C. B., Fundamentals of Analytic Number Theory, Science Press, Beijing (1991), Chinese. (1991) MR2954332
  9. Selberg, A., 10.18311/jims/1954/17018, J. Indian Math. Soc., N. Ser. 18 (1954), 83-87. (1954) Zbl0057.28502MR0067143DOI10.18311/jims/1954/17018
  10. Tenenbaum, G., Introduction to Analytic and Probabilistic Number Theory, Cambridge Studies in Advanced Mathematics 46, Cambridge Univ. Press, Cambridge (1995). (1995) Zbl0831.11001MR1342300
  11. Tenenbaum, G., Wu, J., Théorie analytique et probabiliste des nombres: 307 exercices corrigés, Belin, Paris (2014), French. (2014) MR1397501

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