Identity of Zeta function

  • Thread starter mhill
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  • #1
188
1
it is true in general that the sum (density of states for a physicst)

[tex] \sum_{n=0}^{\infty} \delta (x- \gamma _{n}) [/tex]

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

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

Answers and Replies

  • #2
14
0
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.
 

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