Tom Womack on Fri, 12 May 2000 14:20:14 +0100 |
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L-series derivatives |
Is there any particular reason why computing L(s) for an elliptic curve is an in-built command, whilst to compute L' you have to do something like E = ellinit([0,0,0,0,32757]) N = ellglobalred(E)[1] X = 2*Pi/sqrt(N) VV = eint1(X,2^19) WW = ellan(E,2^19) sum(i=1,2^19,2*VV[i]*WW[i]/i) and there's no obvious way of computing L^(r) for higher derivatives? The L-series functions also seem to take an enormous amount of memory in the case where the conductor is reasonably large; I understand that you have to sum sqrt(N) or so terms of the series, but for the above case the conductor is 10^11 and you can sum the 2^19 terms in well under two minutes on a P3/500. Do there exist algorithms which are a bit more memory-efficient, even at the cost of perhaps taking a bit longer? Tom