Can this sum be made?

  • Thread starter tpm
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  • #1
tpm
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Main Question or Discussion Point

Can this sum be made??

let be the sum:

[tex] f(x) = \sum_{\rho}exp(\rho x) [/tex]

where the sum is made over all Non-trivial zeros of [tex] \zeta (s) [/tex]

is the sum 'calculable' i mean:

* the sum converges to the function f(x) for every x (even x big) except perhaps at certain points where f(x) has discontinuities

* If we asume RH then does the result simplifies ??... thanks.

Also i would like to know if [tex] \sum_{n=1}^{\infty} log ( \zeta (ns) [/tex] s >1 converges to a finite value.
 

Answers and Replies

  • #2
Gib Z
Homework Helper
3,346
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2nd question, Yes.
 

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