On the Asymptotic Behaviour of Some Towers of Function Fields over Finite Fields
On the Asymptotic Behaviour of Some Towers of Function Fields over Finite Fields
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DOI：
10.1006/jnth.1996.0147
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发表时间：
1996-12
影响因子：
0.7
通讯作者：
Arnaldo Garcia;H. Stichtenoth
中科院分区：
文献类型：
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作者：
Arnaldo Garcia;H. Stichtenoth
设F_1是一元代数函数域，其常数域是基数为l的有限域。Weil定理指出F1的一次位数N=N（F）满足估计N1 +1+2g 1，（0.1）其中g= g（F）表示F的亏格。众所周知，当g大于l时，Weil界（0.1）不是最优的;见[5，9]。Drinfeld和Vladut [1]证明了如下渐近结果：设Nl（g）：=max[N（F）]| F是F1上亏格为g]的函数域，且A（1）：=lim supg N1（g）g. (0.2)产品编号0147
Let F Fl be an algebraic function field of one variable, whose constant field is the finite field of cardinality l. Weil's theorem states that the number N=N(F ) of places of degree one of F Fl satisfies the estimate N l+1+2g l , (0.1) where g= g(F ) denotes the genus of F. It is well known that for g large with respect to l, the Weil bound (0.1) is not optimal; see [5, 9]. Drinfeld and Vladut [1] proved the following asymptotic result: Let Nl (g) :=max[N(F ) | F is a function field over Fl of genus g], and A(l) :=lim sup g Nl (g) g. (0.2) article no. 0147