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Can this sum be made?

  1. Apr 6, 2007 #1


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    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.
  2. jcsd
  3. Apr 6, 2007 #2

    Gib Z

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    Homework Helper

    2nd question, Yes.
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