在這篇論文中，我們要計算在一個二次的field extension上週期為 的點個數的平均值，其構想和方法主要是參考 [3] 和 [4] 這兩篇論文。我們利用兩種不同的方法去計算這一個平均值，Prime Number Theorem 和Group Action。第一個方法是先計算週期為 的點個數，再利用Prime Number Theorem去計算平均值。第二個方法是去討論這個平均值和Galois group 作用在這些點上的orbit個數間的關係，進而利用這樣的關係計算出此平均值。 In this paper, we compute the average of the number of r-periodic points over a quadratic number ?eld generalizing results in [3] and [4]. We use two di®erent methods, the prime number theorem and group action, to compute the average and compare the result. First method is to counte the number of the primitive r-periodic points. After that we use the prime number theorem to compute the average. And we discuss relationship between the average and the number of orbits in the set of primitive r-periodic points under the Galois action in the second method.
