On May 4, 2009, at 8:57 AM, kcrisman wrote:
> Dear Support,
>
> There are several calculators in reference/lfunctions.html for L-
> functions. However, I am not quite sure what to do if I want a
> "Dirichlet series" coming not from a character nor an elliptic curve,
> e.g. sum mu(n)/n^s for the Moebius mu function. I tried
>
> sage: L = Dokchitser(conductor=1, gammaV=[0], weight=1, eps=1)
> sage: L.init_coeffs('moebius(k)')
> as a very naive try but doesn't seem to evaluate. In particular I'm
> not sure whether a conductor has relevance for this - does it come
> from an EC after all?
No, I don't think this comes from an elliptic curve. This is the
right way to do it, but it seems as if you've got some of the
parameters wrong--this should be close to zero:
sage: L.check_functional_equation()
-0.166126027002134
(Sorry, I don't know off the top of my head what the functional
equation actually is...)
> I honestly don't know how to input this sort of thing into Sage. I
> mostly want to just evaluate it at various points, though showing that
> L*zeta(s)=1 symbolically as well would be very nice!
This could probably be done by some clever manipulations of the euler
product.
- Robert
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