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Russian Dolls Matryoshka Approach to Riemann Hypothesis

  1. Jun 28, 2009 #1
    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! :)
  2. jcsd
  3. Jun 29, 2009 #2


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

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

    I don't know any.
  4. Jun 29, 2009 #3
    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 [tex] U=exp(iuL) [/tex] is related to [tex] exp(-u)d\Psi (e^u) [/tex] here 'd' means teh derivative and Psi is teh Chebyshev function
  5. Jun 29, 2009 #4
    yeah these two I was interested in + Montgomery's pair correlation conjecture breakdown....
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