Skip to main content
SpringerLink
Log in

Oscillation theorems

  • Conference paper
  • First Online:
Analytic Number Theory

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

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

Access this chapter

Log in via an institution
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anderson, Robert J. On the Mertens conjecture for cusp forms, Mathematika 26 (1979), 236–249.

    Article  MathSciNet  MATH  Google Scholar 

  2. Bateman, P. T., Brown, J. W., Hall, R. S., Kloss, K. E., Stemmler, Rosemarie M., Linear relations connecting the imaginary parts of the zeros of the zeta function, in Computers in Number Theory, Academic Press, New York, 1971, 11–19.

    Google Scholar 

  3. Brun, Viggo, La somme des facteurs de Möbius, C.R. Dixième Congrès Math. Scandinaves 1946, 40–53.

    Google Scholar 

  4. Diamond, Harold G., Two oscillation theorems, Lecture Notes in Math. 251 (1972), 113–118.

    Article  MathSciNet  Google Scholar 

  5. -, Changes of sign of π(X)-ei(X), L'Enseignement Mathematique 21 (1975), 1–14.

    MathSciNet  Google Scholar 

  6. Fawaz, A. Y., The explicit formula for L0(X), P. L. M. S. (3) 1 (1951), 86–103.

    Article  MathSciNet  MATH  Google Scholar 

  7. -, On an unsolved problem in the analytic theory of numbers, Quart. J. Math. Oxford Ser. (2) 3 (1952), 282–295.

    Article  MathSciNet  MATH  Google Scholar 

  8. Goldstein, L. J., A necessary and sufficient condition for the Riemann hypothesis for zeta functions attached to eigenfunctions of the Hecke operators, Acta Arith. 15 (1968/69), 205–215.

    MathSciNet  MATH  Google Scholar 

  9. Grosswald, Emil, On some generalizations of theorems by Landau and Polya, Israel J. Math. 3 (1965), 211–220.

    Article  MathSciNet  MATH  Google Scholar 

  10. -, Oscillation theorems, Lecture Notes in Math. 251 (1972), 141–168.

    Article  MathSciNet  MATH  Google Scholar 

  11. Gupta, Hansraj, On a conjecture of Miller, J. Indian Math. Soc. (N. S.) 13 (1949), 85–90.

    MathSciNet  MATH  Google Scholar 

  12. Gupta, H., Cheema, M. S., Gupta, O.P., On Möbius means, Res. Bull. Panjab Univ., no. 42 (1954).

    Google Scholar 

  13. Haselgrove, C. B., A disproof of a conjecture of Polya, Mathematika 5 (1958), 141–145.

    Article  MathSciNet  MATH  Google Scholar 

  14. Ingham, A. E., On two conjectures in the theory of numbers, Amer. J. Math. 64 (1942), 313–319.

    Article  MathSciNet  MATH  Google Scholar 

  15. Jurkat, W., On the Mertens conjecture and related general Ω-theorems, Proc. Symp. Pure Math. 24, A. M. S., Providence, 1973, 147–158.

    Google Scholar 

  16. Lehman, R. Sherman, On Liouville's function, Math. Comp. 14 (1960), 311–320.

    MathSciNet  MATH  Google Scholar 

  17. Neubauer, Gerhard, Eine empirische Untersuchung zur Mertensschen Funktion, Numer. Math. 5 (1963), 1–13.

    Article  MathSciNet  MATH  Google Scholar 

  18. Saffari, Bahman, Sur la fausseté de la conjecture de Mertens, C. R. Acad. Sci. Paris Ser A-B 271 (1970), A1097–A1101.

    MathSciNet  MATH  Google Scholar 

  19. Stark, H. M., A problem in comparative prime number theory, Acta Arith. 18 (1971), 311–320.

    MathSciNet  MATH  Google Scholar 

  20. te Riele, H. J. J., Computations concerning the conjecture of Mertens, J. Reine Angew. Math., 311/312 (1979), 356–360.

    MathSciNet  MATH  Google Scholar 

  21. Terras, Audrey, Fourier Analysis on Symmetric spaces and applications to number theory, to be published. *** DIRECT SUPPORT *** A00J4373 00003

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Tufts University, Tufts, The Netherlands

    Robert J. Anderson

  2. M.I.T., Cambridge, Massachusetts

    H. M. Stark

  3. U.C.S.D, La Jolla, California

    H. M. Stark

Authors
  1. Robert J. Anderson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. M. Stark
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Marvin I. Knopp

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Anderson, R.J., Stark, H.M. (1981). Oscillation theorems. In: Knopp, M.I. (eds) Analytic Number Theory. Lecture Notes in Mathematics, vol 899. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096454

Download citation

  • DOI: https://doi.org/10.1007/BFb0096454

  • 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

Search

Navigation