Bill Allombert on Fri, 21 Sep 2012 00:21:57 +0200

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Re: forprime

On Thu, Sep 20, 2012 at 11:28:30AM +0100, John Cremona wrote:
> Maybe this is an example:  when summing L-series (and related series)
> where the coefficients a(n) are multiplicative, one needs the
> factorization of n in order to compute the coefficient a(n).  I have
> old GP code which does this in order to cpmpute analytic ranks and
> Heegner points on elliptic curves.  This goes back to the days where
> GP did not allow any arrays to have more then (?) 46000 entries, and
> memory was limited, so the whole scheme may be completely redundant
> now that ellan(e,10^6) takes <5s.

Actually, in the course of porting the Heegner code to PARI I have written a
function forellan() that use the Bulher-Gross iteration over the values of
ellan. This function is available in the GIT branch 'bill-forellan'.

? ??forellan

   Executes seq for all a = [a_n,n] where a_n != 0 and 1 <= n <= b, in non-sequential order, the
numbers a_n being the n-th Fourier coefficient of the L-function of the elliptic curve E.

? E=ellinit([1,3]);forellan(E,a,100,print1(a))