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Homework Help: Difficult Zeta Function Proof NEED ANSWER

  1. Jan 24, 2010 #1
    1. The problem statement, all variables and given/known data
    Prove that sum(n=0 to infty, (zeta(it))^(n)) equals zero when the variable (it) is the imaginary part of the nontrivial zeros of the Riemann zeta function that have real part 1/2. For example, it=14.134i. Note: n represents the nth derivative of the zeta function.



    2. Relevant equations



    3. The attempt at a solution
    I tried to approach this problem by expanding using a Euler-MacLaurin expansion, but failed because I obtained the original equation. Any help would be VERY much appreciated.
     
  2. jcsd
  3. Jan 24, 2010 #2
    I really need help in the next hour or so; my proof fell apart at the last minute.
     
  4. Jan 25, 2010 #3
    I changed the format to make the problem easier to read.

    Prove that [tex]\sum_{n=0}^{\infty} f^n(it)[/tex] equals 0 when [tex]it[/tex] is equal to the imaginary part of the zeros of the Riemann Zeta function that have real part 1/2, for example, [tex]it=14.134i[/tex]. Note: [tex]f^n(it)[/tex] is the nth derivative of the Riemann Zeta function
     
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