Czechoslovak Mathematical Journal

, Volume 69, Issue 1, pp 1–10 | Cite as

Sums of Multiplicative Function in Special Arithmetic Progressions

  • Bin FengEmail author


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).


Selberg-Delange method multiplicative function arithmetic progressions 

MSC 2010



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  1. [1]
    Z. Cui, J. Wu: The Selberg-Delange method in short intervals with an application. Acta Arith. 163 (2014), 247–260.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    H. Delange: Sur des formules dues à Atle Selberg. Bull. Sci. Math., II. Ser. 83 (1959), 101–111. (In French.)MathSciNetzbMATHGoogle Scholar
  3. [3]
    H. Delange: Sur des formules de Atle Selberg. Acta Arith. 19 (1971), 105–146. (In French.)MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    P. X. Gallagher: Primes in progressions to prime-power modulus. Invent. Math. 16 (1972), 191–201.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    G. Hanrot, G. Tenenbaum, J. Wu: Averages of certain multiplicative functions over friable integers. II. Proc. Lond. Math. Soc. (3) 96 (2008), 107–135. (In French.)CrossRefzbMATHGoogle Scholar
  6. [6]
    Y.-K. Lau: Summatory formula of the convolution of two arithmetical functions. Monatsh. Math. 136 (2002), 35–45.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    Y.-K. Lau, J. Wu: Sums of some multiplicative functions over a special set of integers. Acta Arith. 101 (2002), 365–394.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    C. D. Pan, C. B. Pan: Fundamentals of Analytic Number Theory. Science Press, Beijing, 1991. (In Chinese.)Google Scholar
  9. [9]
    A. Selberg: Note on a paper by L. G. Sathe. J. Indian Math. Soc., N. Ser. 18 (1954), 83–87.zbMATHGoogle Scholar
  10. [10]
    G. Tenenbaum: Introduction to Analytic and Probabilistic Number Theory. Cambridge Studies in Advanced Mathematics 46, Cambridge Univ. Press, Cambridge, 1995.zbMATHGoogle Scholar
  11. [11]
    G. Tenenbaum, J. Wu: Théorie analytique et probabiliste des nombres: 307 exercices corrigés. Belin, Paris, 2014. (In French.)Google Scholar

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsYangtze Normal UniversityChongqingPR China

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