Russian Dolls Matryoshka Approach to Riemann Hypothesis

**HermitianMonk** · Jun29-09, 12:59 AM

Well we know what matryoshka dolls are? Those nested dolls one inside another. I am a mere laymen and amateur that's why I am using descriptive terms instead of math rigor. So what should the approach be:

If RH nest Hilbert-Polya conjecture, then what things nest HP conjecture? And ad infinitum...

I chose HP conjecture because it seems to be the hottest thang right now since Montgomery's meeting with Dyson about eigenvalues of random Hermitian matrices corresponding to the zeros of RH....

Thus my questions are twofold:

1. An elaboration on Hilbert-Polya conjecture (I did do forum search!).
2. Are there further 'sub-sets' that are embedded in HP conjecture, proving which will in turn prove RH by moving all the cogwheels and gears?

Thanks! :)

**CRGreathouse** · Jun29-09, 10:14 AM

Originally Posted by HermitianMonk

I am a mere laymen and amateur that's why I am using descriptive terms instead of math rigor.

Being a layman is fine. Using descriptive terms instead of rigorous math... that's harder.

Originally Posted by HermitianMonk

If RH nest Hilbert-Polya conjecture, then what things nest HP conjecture? And ad infinitum...

I take it by "nest" you mean "is/are implied by"?

Originally Posted by HermitianMonk

2. Are there further 'sub-sets' that are embedded in HP conjecture, proving which will in turn prove RH by moving all the cogwheels and gears?

I don't know any.

**zetafunction** · Jun29-09, 10:36 AM

from the functional point of view ,which is commont to both physicist and mathematicians

1. RH is equivalent to finding a Riemann surface whose geodesic lenghts are the primes , and the eigenvalues of its Laplacian are 1/4+it^2 , being 't' the imaginary part of the zeros

2. RH is equivalent to finding a chaotic Hamiltonian with lenght of closed orbits proportional to primes

3. RH and Hilbert-Polya approach are equivalent to finding a linear operator L so the Trace of

is related to $LaTeX Code: exp(-u)d\\Psi (e^u)$ here 'd' means teh derivative and Psi is teh Chebyshev function

**HermitianMonk** · Jun29-09, 11:21 PM

Originally Posted by zetafunction

2. RH is equivalent to finding a chaotic Hamiltonian with lenght of closed orbits proportional to primes

3. RH and Hilbert-Polya approach are equivalent to finding a linear operator L so the Trace of is related to $LaTeX Code: exp(-u)d\\Psi (e^u)$ here 'd' means teh derivative and Psi is teh Chebyshev function

yeah these two I was interested in + Montgomery's pair correlation conjecture breakdown....