On May 4, 2009, at 10:52 AM, Robert Bradshaw wrote:
> 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...)
Actually, Dokchitser's algorithm only handles functions with finitely
many poles, so it won't be able to handle this if L(s) = 1/zeta(s).
- Robert
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