Advertisement

manuscripta mathematica

, Volume 72, Issue 1, pp 205–211 | Cite as

Der ĉebotarev’sche dichtigkeitssatz und ein analogon zum dirichlet’schen primzahlsatz für algebraische funktionenkörper

  • Franz Halter-Koch
Article

Abstract

We improve the remainder term in Čebotarev’s density theorem for algebraic function fields by a logarithmic factor. With aid of this, we deduce an analogon of Dirichlet’s theorem on primes in arithmetic progressions for holomorphy rings of algebraic function fields with best possible remainder term.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    M. D. Fried, M. Jarden,Field Arithmetic, Springer 1986Google Scholar
  2. [2]
    F. Halter-Koch,A note on ray class fields of global fields, Nagoya Math. J.120 (1990), 61–66zbMATHMathSciNetGoogle Scholar
  3. [3]
    F. Halter-Koch, W. Müller,Quantitative aspects of non-unique factorization: A general theory with applications to algebraic function fields, J. Reine Angew. Math.Google Scholar
  4. [4]
    M. Kruse, H. Stichtenoth,Ein Analogon zum Primzahlsatz für algebraische Funktionenkörper, Manuscripta Math.69 (1990), 219–221zbMATHMathSciNetGoogle Scholar
  5. [5]
    K. Prachar,Primzahlverteilung, Springer 1957Google Scholar
  6. [6]
    J. Riordan,Combinatorial Identities, J. Wiley, New York 1968zbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Franz Halter-Koch
    • 1
  1. 1.Institut für MathematikKarl-Franzens-UniversitätGrazÖsterreich

Personalised recommendations