# Identity of Zeta function

1. Dec 5, 2008

### mhill

it is true in general that the sum (density of states for a physicst)

$$\sum_{n=0}^{\infty} \delta (x- \gamma _{n})$$

is related to the value $$\frac{ \zeta '(1/2+is)}{\zeta (1/2+is)}+\frac{ \zeta '(1/2-is)}{\zeta (1/2-is)}$$

here the 'gamma' are the imaginary parts of the non-trivial zeros of Riemann zeta function

2. Dec 14, 2008

### rscosa

Hi,
I think the problem is not well-defined, the first part is a functional and the second a function. Please, be more especific. But I guess there is some relation like this.