Re: class number of IQ(2^{1/n})

[Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>]

On Wed, Aug 27, 2008 at 11:21:30AM +0200, Bill Allombert wrote:
> On Sat, Aug 23, 2008 at 04:24:53PM +0200, herbert granzow wrote:
> > Are there statements about the class number of IQ(2^{1/n}) (beside general
> > theorems like the Minkowski bound)?
> > 
> > Using PARI, I found that it equals 1 for n <= 46.
> > 
> > Does someone know a n for which the class number is > 1?
> > 
> > 
> > It can't be known that it is always 1 since this would solve an open
> > question.
> 
> I do not have an answer for you. I just computed the class number for
> 48<=n<=52 with a slightly modified version of bnfinit and it is always 1.

... and it is also 1 for n=47 and n=54.

Cheers,
Bill.