论文标题
用对称的Galois组在随机多项式上的范德华顿猜想的注释
A note on the van der Waerden conjecture on random polynomials with symmetric Galois group for function fields
论文作者
论文摘要
令f（x）= x^n +（a [n-1] t + b [n-1]）x^（n-1） + ... + ... +（a [0] t + b [0]）在x中为恒定度n，t in t in t and t in t in t，其中所有a [i]，b [i] b [i]均随机和均匀地从q元素的q元素的有限fielt gf（q）中选择。然后，f对合理函数场GF（q）（t）上F的GALOIS组的概率是N元素上的对称组S（N）为1 -O（1/Q）。此外，gf（q）（q）（t）上的f（x）的Galois组不是s（n）的> = 1/q，对于n> = 3和> 1/q -1/q -1/（2q^2），对于n = 2。
Let f(x) = x^n + (a[n-1] t + b[n-1]) x^(n-1) + ... + (a[0] t + b[0]) be of constant degree n in x and degree <= 1 in t, where all a[i],b[i] are randomly and uniformly selected from a finite field GF(q) of q elements. Then the probability that the Galois group of f over the rational function field GF(q)(t) is the symmetric group S(n) on n elements is 1 - O(1/q). Furthermore, the probability that the Galois group of f(x) over GF(q)(t) is not S(n) is >= 1/q for n >= 3 and > 1/q - 1/(2q^2) for n = 2.
