Progress Towards Counting D_5 Quintic Fields

Details Progress Towards Counting D_5 Quintic Fields Progress Towards Counting D_5 Quintic Fields

2011-07-20

arxiv.org/abs/1107.4111v4

Mathematics

Number Theory

7 pages

Scientific paper

Let $N(5,D_5,X)$ be the number of quintic number fields whose Galois closure has Galois group $D_5$ and whose discriminant is bounded by $X$. By a conjecture of Malle, we expect that $N(5,D_5,X) \sim C X^{1/2}$ for some constant $C$. The best known upper bound is $N(5,D_5,X)\ll X^{3/4 + \epsilon}$, and we show this could be improved by counting points on a certain variety defined by a norm equation; computer calculations give strong evidence that this number is $\ll X^{2/3}$. Finally, we show how such norm equations can be helpful by reinterpreting an earlier proof of Wong on upper bounds for $A_4$ quartic fields in terms of a similar norm equation.

Affiliated with

Also associated with

No associations

Rating

Progress Towards Counting D_5 Quintic Fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Progress Towards Counting D_5 Quintic Fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Progress Towards Counting D_5 Quintic Fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-687083