Bill Allombert on Wed, 27 Aug 2008 11:28:19 +0200

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

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.


P.S.: For some reason, four copies of your post were received byt the
list. See