Re: Lists of class numbers of imaginary quadratic fields - help pls?

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

On Wed, Oct 22, 2008 at 01:36:21PM +0100, James Wanless wrote:
> Hi,
> 1) Thanks to the devs for PARI/GP, I have already found it very  
> useful and fun, and if it can solve my problem here I'll be very  
> grateful!
> 2) I'm trying to use/modify the following program (from OEIS) to  
> generate above lists (up to h=50 or even above, hopefully):
> { bnd = 10000; S = vector(10, X, []); for (i = 1, bnd, if  
> (issquarefree(i), n = qfbclassno(if(i%4==3, -i, -4*i)); if (n<11, S 
> [n] = concat(S[n], i), ), )); }
> 3) I'm using gp V2.3 on a PPC iMac G5 (in case that's relevant)
> 4) When I compare lists for the first few h, there is a good, but not  
> perfect match with the tables at http://mathworld.wolfram.com/ 
> ClassNumber.html
> Why is that, please? And which should I trust? [or are they both  
> right and there is some mapping involving genera I need to consider?]

It seems the problem is that you should store the discriminant and not i,

 { bnd = 10000; S = vector(10, X, []); for (i = 1, bnd, if
 (issquarefree(i), d = if(i%4==3, -i, -4*i); n = qfbclassno(d); if (n<11, S
 [n] = concat(S[n], -d), ), )); }

Second qfbclassno is known to be unreliable. Use 
n = quadclassunit(d).no
instead. However your program seems to return correct results even while
using qfbclassno.

Cheers,
Bill.