Constructing function fields¶with many rational places via the Carlitz module |
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| Authors: | Max Gebhardt |
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| Institution: | 1.FR 6.1. Mathematik, Universit?t des Saarlandes, Postfach 15 11 50,?66041 Saarbrücken, Germany. e-mail: gebhardt@math.uni-sb.de,DE |
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| Abstract: | We consider certain decomposition fields in extensions of ?q (Z) by the Carlitz module and give formulas for their genera and numbers of rational places, suitable for automatic computations.
By extensive calculations we found some function fields which have more rational places than the known examples of the respective
genus.
Received: 7 September 2001/ Revised version: 19 October 2001 |
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| Keywords: | Mathematics Subject Classification (2000): 11G20 11Y40 11R58 |
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