Skip to main content
Log in

The connection between the zeros of the ζ-function and sequences(g(p)), p prime, mod 1

  • Published:
Monatshefte für Mathematik Aims and scope Submit manuscript

Abstract

In this paper we give the connection between the zeros of the ζ-function and sequences(g(p)), p prime, mod 1 ifg(x)x σ for α≠0, σ>0 or ifg(X) is a polynomial in ℝ.

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

References

  1. De Bruijn, N. G.: Asymptotic Methods in Analysis. Amsterdam: North Holland Publishing Co. 1958.

    Google Scholar 

  2. Hardy, G. H.: Hardy, Collected Papers II, pp. 162–177. Oxford: At the Clarendon Press. 1967.

    Google Scholar 

  3. Hlawka, E.: Über die Gleichverteilung gewisser Folgen, welche mit den Nullstellen der ζ-Funktion zusammenhängen. Sitzber. österr. Akad. Wiss., Abt. II,184, 459–471 (1975).

    Google Scholar 

  4. Landau, E.: Über die Nullstellen der ζ-Funktion. Math. Ann.71, 548 (1912).

    Google Scholar 

  5. Leitmann, D.: On the uniform distribution of some sequences. J. Lond. Math. Soc.14, 181–184 (1975).

    Google Scholar 

  6. Markhushevitsch, A. I.: Theory of Functions of a Complex Variable II. Englewood Cliffs, N.Y.: Prentice-Hall. 1965.

    Google Scholar 

  7. Pjateckij-Sapiro, I. I.: On the distribution of the prime numbers in sequences of the form [f(n)]. (Russ.). Math. Sb.30, 559–566 (1953).

    Google Scholar 

  8. Prachar, K.: Primzahlverteilung. Grundlehren der Math. Wiss., Bd. 91, p. 231. Berlin-Heidelberg-New York: Springer. 1957.

    Google Scholar 

  9. Rademacher, H.: Collected Papers, Vol. II, p. 455. Cambridge, Massachusetts, and London: MIT-Press. 1974.

    Google Scholar 

  10. Stux, I.: On the uniform distribution of prime powers. Comm. Pure and Appl. Math.27, 729–740 (1974).

    Google Scholar 

  11. Titchmarsh, E. C.: The Theory of the Riemann Zeta Function, p. 190. Oxford: at the Clarendon Press. 1951.

    Google Scholar 

  12. Vinogradov, I. M.: On an estimate of trigonometric sums with prime numbers. (Russ.) Izv. Akad. Nauk SSSR, Ser. Mat.12, 225–248 (1948).

    Google Scholar 

  13. Wolke, D.: Zur Gleichverteilung einiger Zahlenfolgen. Math. Z.142, 181–184 (1975).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Schoißengeier, J. The connection between the zeros of the ζ-function and sequences(g(p)), p prime, mod 1. Monatshefte für Mathematik 87, 21–52 (1979). https://doi.org/10.1007/BF01470936

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01470936

Navigation