Skip to main content

On the representation of the summatory functions of a class of arithmetical functions

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 899))

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. B.C. Berndt, Identities involving the coefficients of a class of Dirichlet series I, Trans. Amer. Math. Soc., 137 (1969), 345–359.

    Article  MathSciNet  MATH  Google Scholar 

  2. -, On the average order of a class of arithmetical functions, I, J. Number Theory 3 (1971), 184–203.

    Article  MathSciNet  MATH  Google Scholar 

  3. -, Identities involving the coefficients of a class of Dirichlet series VII, Trans. Amer. Math. Soc., 201 (1975), 247–261.

    Article  MathSciNet  MATH  Google Scholar 

  4. K. Chandrasekharan, Arithmetical Functions, Springer-Verlag, New York, 1969.

    MATH  Google Scholar 

  5. K. Chandrasekharan and R. Narasimhan, Hecke's functional equation and arithmetical identities, Ann. Math. 74 (1961), 1–23.

    Article  MathSciNet  MATH  Google Scholar 

  6. -, Functional equations with multiple gamma factors and the average order of arithmetical functions, Ann. Math., 76 (1962), 93–136.

    Article  MathSciNet  MATH  Google Scholar 

  7. -, Approximate functional equations for a class of zeta-functions, Math. Ann. 152 (1963), 30–64.

    Article  MathSciNet  MATH  Google Scholar 

  8. J.L. Hafner, New omega theorems for two classical lattice point problems, Invent. Math. 63 (1981), 181–186.

    Article  MathSciNet  MATH  Google Scholar 

  9. G.H. Hardy, On the expression of a number as the sum of two squares, Quart. J. Math., 46 (1915), 263–283.

    MATH  Google Scholar 

  10. -, On Dirichlet's divisor problem, Proc. London Math. Soc. (2) 15 (1916), 1–25.

    MATH  Google Scholar 

  11. -, The average order of the arithmetical functions P(x) and Δ(x), Proc. London Math. Soc. (2) 15 (1916), 192–213.

    MathSciNet  MATH  Google Scholar 

  12. E. Landau, Einführung in die elementare und analytische Theorie der algebraischen Zahlen und der Ideale, Chelsea, New York, 1949.

    MATH  Google Scholar 

  13. G. Szegö and A. Walfisz, Uber das Piltzsche Teilerproblem in algebraischen Zahlkörpern (Erste Abhandlung), Math. Zeit. 26 (1927), 138–156.

    Article  MATH  Google Scholar 

  14. G. Voronoï, Sur une fonction transcendente et ses applications à la sommation de quelque series, Ann. Sci. Ecole Norm. Sup. (3) 21 (1904), 207–267, 459–553.

    MathSciNet  Google Scholar 

  15. G.N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed., Cambridge Univ. Press, Cambridge, 1952.

    Google Scholar 

  16. A. Zygmund, On trigonometric integrals, Ann. Math., 48 (1947), 393–440.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Marvin I. Knopp

Additional information

This paper is dedicated to Professor Emil Grosswald for his incalculable contribution to the body of mathematical knowledge and to the community of mathematical scientists.

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Hafner, J.L. (1981). On the representation of the summatory functions of a class of arithmetical functions. In: Knopp, M.I. (eds) Analytic Number Theory. Lecture Notes in Mathematics, vol 899. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096458

Download citation

  • DOI: https://doi.org/10.1007/BFb0096458

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11173-3

  • Online ISBN: 978-3-540-38953-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics