Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Based on the graphic in the MathWorld article on the quintic equation it seems very likely that following statement is either true or trivially false in a way that can be easily remedied by adding an additional hypothesis:

Let $A_N$ be the set of degree $n$ polynomials $f(x)$ with integer coefficients $a_0, a_1, ... a_n$ such that $|a_i| < N$. Let $S_N$ be the fraction of these that have Galois group $S_n$. Then as $N \rightarrow \infty$ , $S_N \rightarrow 1$.

It also seems likely that this result follows from well known results: how does one prove it?

share|improve this question
6  
Thoroughly discussed on MO: mathoverflow.net/questions/58397/… –  Qiaochu Yuan Jan 3 '12 at 6:15

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.