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Ein analogon zum Primzahlsatz für algebraische Funktionenkörper

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Abstract

LetF be an algebraic function field of one variable over a finite field\(\mathbb{F}_q \). We prove that

$$ \pi _F (x) \sim \frac{q} {{q - 1}} \cdot \frac{x} {{log_q (x)}},x = q^n \to \infty , $$

where π F (x) denotes the number of prime divisors ofF of norm≤x.

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Literatur

  1. E. Bombieri, Counting points on curves over finite fields. Sem. Bourbaki 1972/73, Exp. 430, Springer LNM 383 (1974), 234–241

    Article  MathSciNet  Google Scholar 

  2. K. Chandrasekharan, Einführung in die Analytische Zahlentheorie. Springer LNM 29 (1966)

  3. J. Knopfmacher, Analytic Arithmetic of Algebraic Function Fields. M. Dekker Lecture Notes in Pure and Applied Math. no. 50, New York 1979

  4. H. Reichardt, Der Primdivisorsatz für algebraische Funktionenkörper über einem endlichen Konstantenkörper. Math. Z.40 (1936), 713–719

    Article  MATH  MathSciNet  Google Scholar 

  5. A. Weil, Sur les courbes algébriques et les variétés qui s'en déduisent. Act. Sci. Ind., no. 1041, Hermann, Paris, 1948

    Google Scholar 

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Kruse, M., Stichtenoth, H. Ein analogon zum Primzahlsatz für algebraische Funktionenkörper. Manuscripta Math 69, 219–221 (1990). https://doi.org/10.1007/BF02567920

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  • DOI: https://doi.org/10.1007/BF02567920

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