有限域上单变量代数函数域中的素数定理

Prime Number Theorem of an Algebraic Function Field of Dimension 1 over a Finite Field

设q是素数的幂次,Fq为一有限域;F为Fq上的单变量代数函数域．在这篇文章中我们证明了下面的素数定理,■其中logqx以q为底的对数,这一结果改进了M．Kruse,H．Stichtenoth的结果．

Suppose q is the power of prime number, Fq is a finite field; F is an Algebraic Function Field of Dimension 1 over Fq. In this paper, we proved the following prime number theorem, πF（x）=1/（q-1）.x/logqx＋O（x/log^2qx）.x=q^n→∞ where logq x is an logarithmic which bases on q, this result improved the one of M.Kruse, H.Stichtenoth＇s.