Re: Complex AGM

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

On Wed, Feb 15, 2012 at 03:24:21PM +0000, John Cremona wrote:
> For a definition of what "optimal" means and why it matters for
> elliptic curve period computations, see http://arxiv.org/abs/1011.0914
> 
> I am pretty sure that taking the principal square root will never give
> a sequence converging to zero.  Using the optimal branch always gives
> the largest limit (and hence the smallest periods), though there is al
> ittle more to the question than that.

In theory, I agree that should converge, but in practice (git-9749657)

parisize = 8000000, primelimit = 500509
? agm(.1+I/1000,1)
  ***   at top-level: agm(.1+I/1000,1)
  ***                 ^----------------
  *** agm: the PARI stack overflows !

Cheers,
Bill.