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A generalization of the Artin-Tschebotareff density theorem in positive characteristic

Part of: Multiplicative number theory

Published online by Cambridge University Press:  26 February 2010

Makoto Ishibashi
Makoto Ishibashi
Affiliation:
Iwaki-Meisei University, 1-27-10 Kitahara-cho, Tanashi-shi, Tokyo 188, Japan.
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Abstract

We shall give an explicit form of the Artin-Tschebotareff density theorem in function fields with several variable over finite fields. It may be an analogous prime number theorem in the higher dimensional case.

MSC classification

Secondary: 11N05: Distribution of primes
Type
Research Article
Information
Mathematika , Volume 41 , Issue 2 , December 1994 , pp. 322 - 328
Copyright
Copyright © University College London 1994

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References

1.Artin, Emil. Quadratische Körper im Gebiet der höheren Kongruenzen I.II. Math. Zeit., 19 (1924), 153–246.CrossRefGoogle Scholar
2.Artin, Emil. Über eine neue Art von L-Reihen. Hamb. Abb., (1923), 89–108.CrossRefGoogle Scholar
3.Deligne, Pierre. La conjecture de Wiel, I. Publ. Math. IHES, 43 (1974), 273–307.CrossRefGoogle Scholar
4.Fried, M. and Sacerdote, G.. Solving diophantine problems over all residue class fields of a number field and finite fields. Annals of Math., 104 (1976), 203–233.CrossRefGoogle Scholar
5.Grothendieck, Alexander. Formule de Lefschetz et rationalité des fonction L. Seminaire Bour-baki, 279 (1965).Google Scholar
6.Goldstein, L. J.. Analytic Number Theory (Prentice-Hall, 1971).Google Scholar
7.Ishibashi, Makoto. Effective version of the Tschebotareff density theorem in function fields over finite fields. Bull London Math. Soc., 24 (1992), 52–56.CrossRefGoogle Scholar
8.Lang, Serge and Weil, Andre. Number of points of varieties in finite fields. Amer. J. of Math., 76 (1954), 819–827.CrossRefGoogle Scholar
9.Reichardt, Hans. Der Primdivisorsatz für algebraische Funktionenkörper uber einem endlichen Konstantenkörper. Math. Zeit., 40 (1936), 713–719.CrossRefGoogle Scholar
10.Serre, J. P.. Zeta and L-functions. In Arithmetical Algebraic Geometry. Edited by Schilling, O. F. G. (1965), 82–92.Google Scholar
11.Freitag, E. and Kiehl, R.. Etale cohomology and the Weil conjecture (Springer, 1988).CrossRefGoogle Scholar