Is V. Mangoldt formula just a trace?...

Extracted from the webpage Chebyshev function - Wikipedia, the free encyclopedia

If we differentiate the expression inside V. Mangoldt formula we get:

1-df-(x^3 -x)^{-1}= Sum(r)x^{r-1} but if RH is true then r (Non trival zeros) are of the form r=1/2+iE(n) , multiplying both sides by x^{0.5} and putting x=exp(u) we have just a "Partition function" which is just the trace of a certain operator

Z=Tr{e^{iuH}) where f= Chebyshev function d=differential operator.

A better explanation is inside this webpage....or in the paper: (arxiv)

http://arxiv.org/ftp/math/papers/0607/0607095.pdf

Where the author relates Statistical Mechanics and Number Theory....:confused: :confused: although for me is a bit confusing.