Summary
For an algebraic function fieldF having a finite constant field, letg(F) (resp.N(F)) denote the genus ofF (resp. the number of places ofF of degree one). We construct a tower of function fields\(F_1 \subseteq F_2 \subseteq F_3 \subseteq \ldots \) over\(\mathbb{F}_{q^2 } \) such that the ratioN(F i )/g(F i ) tends to the Drinfeld-Vladut boundq−1.
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Oblatum 5-XII-1994 @ 2-II-95
This paper was written when the second author was visiting the Instituto de Matemática Pura e Aplicada, Rio de Janeiro (July–Sept. 1994). This visit was supported by BMFT and CNPq.
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Garcia, A., Stichtenoth, H. A tower of Artin-Schreier extensions of function fields attaining the Drinfeld-Vladut bound. Invent Math 121, 211–222 (1995). https://doi.org/10.1007/BF01884295
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DOI: https://doi.org/10.1007/BF01884295