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Drinfeld Modules of Rank 1 and Algebraic Curves with Many Rational Points

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Abstract.

 We construct algebraic curves C defined over a finite prime field such that the number of -rational points of C is large relative to the genus of C. The methods of construction are based on the relationship between algebraic curves and their function fields, as well as on narrow ray class extensions obtained from Drinfeld modules of rank 1.

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Authors and Affiliations

  1. Austrian Academy of Sciences, Wien, Austria, , , , , , AT

    Chaoping Xing & Harald Niederreiter

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  1. Chaoping Xing
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  2. Harald Niederreiter
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Received 21 July 1997; in revised form 5 February 1998

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Xing, C., Niederreiter, H. Drinfeld Modules of Rank 1 and Algebraic Curves with Many Rational Points. Mh Math 127, 219–241 (1999). https://doi.org/10.1007/s006050050036

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  • DOI: https://doi.org/10.1007/s006050050036

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