Skip to main content
Log in

Abstract

A proof that the Riemann zeta-function ζ(σ+ it) has no zeros in the region where R=9.65 and T=12.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Literature cited

  1. E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, Oxford University Press, Oxford (1953).

    Google Scholar 

  2. K. Prakhar, The Distribution of Prime Numbers [in Russian], Moscow (1967).

  3. A. Walfisz, Weilsche Exponentialsummen in der Neueren Zahlentheorie, Berlin (1963).

  4. A. M. Turing, “Some calculations of the Riemann zeta-function,” Proc. London Math. Soc,3, 99 (1953).

    Google Scholar 

  5. D. H. Lehmer, “On the roots of the Riemann zeta-function,” Acta Math.,95, 291–298 (1956).

    Google Scholar 

  6. D. H. Lehmer, “Extended computations of the Riemann zeta-function,” Mathematika,3, 102–108 (1956).

    Google Scholar 

  7. N. A. Meller, “Calculations concerning the verification of the Riemann hypothesis,” Dokl. Akad. Nauk SSSR,123, 246–248 (1958).

    Google Scholar 

  8. C. B. Haselgrove in collaboration with F. C. P. Miller, Tables of the Riemann Zeta-Function, Royal Soc. Math. Tables 6, Cambridge (1960).

  9. R. S. Lehman, “Separation of zeros of the Riemann zeta-function,” Math. Comp.,20, 523 (1966).

    Google Scholar 

  10. F. B. Rosser, L. Schoenfeld, and J. M. Yohe, Rigorous Computations and the Zeros of the Riemann Zeta-Function, IFJP Congress, 1968, Amsterdam (1968), pp. 13–18.

  11. Ch.-J. de la Vallée Poussin, “Sur la fonction de Riemann et le nombre des nombres premiers inférieurs à une limite donnée,” Mémoires Couronnés et Autres Mémoires Publiés par l'Académie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique,59, 1–74 (1899).

    Google Scholar 

  12. B. Rosser, “The n-th prime is greater than n log n,” Proc. London Math. Soc, (2),45, 21–44 (1939).

    Google Scholar 

  13. B. Rosser, “Explicit bounds for some functions of prime numbers,” Amer. J. Math.,63, 211–232 (1941).

    Google Scholar 

  14. E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, Leipzig und Berlin (1909).

  15. H. Westphal, “Über die Nullstellen der Riemannschen Zetafunction im Kritischen Streifen,” Schriften des Math. Seminars und des Instituts für Angewandte Math, der Universitat Berlin,4, No. 1, 1–31 (1938).

    Google Scholar 

  16. J. B. Rosser and L. Schoenfeld, “Approximate formulas for some functions of prime numbers,” Illinois J. Math.,6, 64–94 (1962).

    Google Scholar 

  17. S. B. Stechkin, “Some extremal properties of positive trigonometric polynomials,” Matem. Zametki.,7, No. 4, 411–422 (1970).

    Google Scholar 

  18. L. Bieberbach, Lehrbuch der Funktionentheorie, Vol. 1, Berlin (1921).

  19. A. E. Ingham, The Distribution of Prime Numbers, Cambridge University Press, Cambridge (1936).

    Google Scholar 

  20. H. von Mangoldt, “Zu Riemanns Abhandlung Über die Anzahl der Primzahlen unter Einer Gegebenen Grosse,” J. Reine und Angew. Math.,114, 255–305 (1895).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Translated from Matematicheskie Zametki, Vol. 8, No. 4, pp. 419–429, October, 1970.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Stechkin, S.B. Zeros of the Riemann zeta-function. Mathematical Notes of the Academy of Sciences of the USSR 8, 706–711 (1970). https://doi.org/10.1007/BF01104369

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01104369

Navigation