Abstract
We prove that if there exists a maximal function field of one variable of genusg over\(\mathbb{F}_{q^2 } \), theng≤(q−1) 2/4 org=qr/2 withq−1/2≤r≤q−1.
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This work was finished while the first author visited FB 6 Mathematik und Informatik, Universität GH Essen with the support of the Alexander von Humboldt Foundation of Germany.
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Xing, C., Stichtenoth, H. The genus of maximal function fields over finite fields. Manuscripta Math 86, 217–224 (1995). https://doi.org/10.1007/BF02567990
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DOI: https://doi.org/10.1007/BF02567990