|Bill Allombert on Fri, 21 Sep 2012 00:21:57 +0200|
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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 forellan(E,a,B,seq): 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)) [-3,9][9,81][2,5][-6,45][-1,25][2,7][-6,63][4,35][-3,49][-6,11][-12,55][-12,77][18,99][-1,13][-2,65][-2,91][1,17][2,85][-1,19][-2,95][-3,23][-6,29][-9,31][-1,37][3,41][-3,43][-6,47][6,53][5,59][7,61][3,67][8,71][-6,73][-4,79][6,83][10,89][1,97] Cheers, Bill.