Hey, so following problem:

I want to express

as a Dirichlet series, i.e. as a series of the form

where is any complex sequence.

Who can help?

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- Feb 23rd 2010, 04:31 AMEinStoneRiemann Zeta function
Hey, so following problem:

I want to express

as a Dirichlet series, i.e. as a series of the form

where is any complex sequence.

Who can help? - Feb 23rd 2010, 05:02 AMtonio

I'm not sure I follow you, but what if you define ? This certainly will do the trick...(Cool)

Now perhaps you're on to something else, since is the first step to express the zeta function as an Euler product, so...well, so who knows what you're on to actually.

Tonio - Feb 23rd 2010, 05:04 AMNonCommAlg
- Feb 23rd 2010, 06:39 AMEinStone
- Feb 23rd 2010, 06:50 AMNonCommAlg

- Feb 23rd 2010, 07:03 AMEinStone
- Feb 23rd 2010, 07:44 AMtonio
- Feb 23rd 2010, 03:09 PMEinStone
Ah too easy xD.

So I have another really similar problem. Namely expressing

as a Dirichlet series.

I tried again to split up the n on three series for the modulo 3 residues, but it somehow didnt work. Do you have an idea?

- Feb 24th 2010, 09:30 AMNonCommAlg