Skip to main content

On the Distribution of Numbers Prime to n

  • Chapter
Number Theory and Analysis

Abstract

The problem how the numbers prime to n and less than n are distributed asymptotically for large values of n has been raised by P. Erdös ([1], see also [2], [3] and [4]). Recently C. Hooley ([5], [7]) has investigated this problem and obtained very interesting results. The present paper is based entirely on Hooley’s work: we shall deduce some further consequences of his results.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. P. Erdös, The difference of consecutive primes, 16 (1940), 438–441.

    Google Scholar 

  2. P. Erdös, On the integers relatively prime to n and on a number-theoretic function considered by Jacobsthal, Math. Scand. 10 (1962), 163–170.

    MathSciNet  MATH  Google Scholar 

  3. P. Erdös, Some unsolved problems, MTA Mat. Kut. Int. Közl. 6 (1961), 221–254.

    MATH  Google Scholar 

  4. P. Erdös, Some recent advances and current problems in number theory, Lectures on Modern Mathematics, Vol. 3. p. 196–244, Wiley, 1965.

    Google Scholar 

  5. C. Hooley, On the difference of consecutive numbers prime to n, Acta Arithmetica 8 (1963), 343–347.

    MathSciNet  MATH  Google Scholar 

  6. C. Hooley, On the difference between consecutive numbers prime to n, II, Publications Mathematicae 12 (1965), 39–49.

    MathSciNet  MATH  Google Scholar 

  7. C. Hooley, On the difference between consecutive numbers prime to n, III, Math. Z. 90 (1965), 355–364.

    MathSciNet  MATH  Google Scholar 

  8. A. Rényi, On an extremal property of the Poisson process, Annals of the Institute of Stat. Math. 16(1964), 129–133.

    Article  Google Scholar 

  9. A. Rényi, Remarks on the Poisson process, Studia Sci. Math. Hung. 2 (1967), 119–124.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Paul Turán

Rights and permissions

Reprints and permissions

Copyright information

© 1969 Springer Science+Business Media New York

About this chapter

Cite this chapter

Rényi, A. (1969). On the Distribution of Numbers Prime to n . In: Turán, P. (eds) Number Theory and Analysis. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4819-5_19

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-4819-5_19

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7184-7

  • Online ISBN: 978-1-4615-4819-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics