# Homework Help: Difficult Zeta Function Proof NEED ANSWER

1. Jan 24, 2010

### seanhbailey

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. Jan 24, 2010

### seanhbailey

I really need help in the next hour or so; my proof fell apart at the last minute.

3. Jan 25, 2010

### seanhbailey

I changed the format to make the problem easier to read.

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