Re: once again

how about this ?

it has derivative F'(z) = zeta(z)
F(2)= 2 + sum n=2 -> infinity [ln(n)^-1]*n^(-2)
F(1) is a pole

where are the zero's ?

or even this

F(z)= z + sum n=2 -> infinity [ln(n)^-1]*n^(-z)
F(1) is a pole

no need for continuations and stuff

only looking for the zero's

also intresting:

1) find Taylor or Dirichlet series for F (if they exist)
2) find functional equations for F (if they exist)
3) find regions where F has no zeroes
4) find a number-theoretic interpretation for
"F(s)=0"

regards
tommy1729
.

Relevant Pages

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  • Re: once again
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  • Re: once again
    ... Now your question of research is to find all zeroes ... But I'm quite sure that I left out the pole condition ... something more straightforward to fix the integration ... Do you wonder why your seemingly minor modifications ...
    (sci.math)
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