#4475: create a native Sage implementation of Dokchitser's L-functions algorithm
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Reporter: was | Owner: was
Type: enhancement | Status: new
Priority: major | Milestone: sage-3.2.1
Component: number theory | Resolution:
Keywords: |
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Comment (by robertwb):
I attached a wrapping of the G_s(t) terms, and got it working (at least it
computes the Riemann zeta function correctly). There is an off-by-one typo
in formula (10) of the paper (the computation of the poles should be {{{rj
k!/(pj - s)^(k+1)}}}). However, this fix still didn't give the right
answer so I examined Dokchister's code and he has an extra summation over
the poles (very last function of computel.gp) and I couldn't figure out
where that was coming from.
The weight and the exponential factor are used for calculating the
intermediate precision/number of terms needed in the various series
related to computing G_s(t), which turns out to be the bulk of the work of
{{{initLdata}}}, so it made things a lot cleaner to simply call that
function for now.
It should be noted that to compute the value at s it may be necessary to
compute the power series at s and then evaluate to let the poles and zeros
of the gamma factor cancel out poles/zeros of L* appropriately.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4475#comment:2>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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