A Comparision of the Number of Rational Places of Certain Function Fields to the Hasse-Weil Bounds

We give explicitly the number of rational places of certain function fields in terms of the reciprocals of the zeros of the function fields in question. The results are then compared with the Hasse-Weil bounds by using the approximation theorems of Dirichlet and Kronecker and it turns out that in many of these function fields the number of rational places is near the upper Hasse-Weil bound. Keywords:Function fields, Diophantine approximation, Exponential sums.