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A Comparision of the Number of Rational Places of Certain Function Fields to the Hasse-Weil Bounds

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Abstract.

We give explicitly the number of rational places of certain function fields in terms of the reciprocals of the zeros of the function fields in question. The results are then compared with the Hasse-Weil bounds by using the approximation theorems of Dirichlet and Kronecker and it turns out that in many of these function fields the number of rational places is near the upper Hasse-Weil bound.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Vaasa, 700, 65101, Vaasa, Finland

    Marko J. Moisio

  2. Department of Mathematical Sciences, University of Oulu, 3000, 90014, Oulu, Finland

    Keijo O. Väänänen

Authors
  1. Marko J. Moisio
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  2. Keijo O. Väänänen
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Correspondence to Marko J. Moisio.

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Keywords: Function fields, Diophantine approximation, Exponential sums.

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Moisio, M., Väänänen, K. A Comparision of the Number of Rational Places of Certain Function Fields to the Hasse-Weil Bounds. AAECC 14, 341–359 (2004). https://doi.org/10.1007/s00200-003-0143-3

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  • DOI: https://doi.org/10.1007/s00200-003-0143-3

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