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HIlbert-Polya conjecture proof of RH through Quantum mechanics

  1. Oct 18, 2007 #1
    The main idea to prove RH through the HIlbert Polya conjecture , is
    finding a Hamiltonian H=p^2 V(x) (QM) , so its energies are
    precisely the imaginary parts of the Non-trivial zeros.

    Using the Von Mangoldt formula for the Chebyshev function,
    differentiating respect to x , and setting x=exp(u) we can get an
    expression for the Trace of the operator exp(iuH).

    Using the WKB expansion we can obtain an integral equation for V(x) .


    To se the original manuscript published at the 'General Science

    If we consider that V. Mangoldt formula is completely correct, then
    the proposed trace for exp(iuH) given at the paper is just the ONLY
    possible one, the Nonlinear integral equation can be solved by
    Numerical methods
  2. jcsd
  3. Oct 21, 2007 #2
    There are two problems with this approach before you even get started: 1) The Hilbert Polya CONJECTURE would have to be proved first, and 2) it would then have to be proved that the HP conjecture implied RH.
  4. Oct 25, 2007 #3
    I suppose I should clarify for the one or two of you who haven't figured it out by now -- RH means Riemann Hypothesis, which is one of the hottest unsolved problems in math.
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