HIlbert-Polya conjecture proof of RH through Quantum mechanics

AI Thread Summary
The discussion centers on using the Hilbert-Polya conjecture to prove the Riemann Hypothesis (RH) through quantum mechanics by identifying a Hamiltonian where its energies correspond to the imaginary parts of the non-trivial zeros of the Riemann zeta function. The approach involves applying the Von Mangoldt formula for the Chebyshev function and deriving an expression for the trace of the operator exp(iuH). A WKB expansion leads to an integral equation for the potential V(x). However, two significant challenges exist: the need to first prove the Hilbert-Polya conjecture and then demonstrate that it implies RH. The conversation emphasizes the complexity and significance of these mathematical concepts.
josegarc
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) .

www.wbabin.net/science/moreta1.pdf

To se the original manuscript published at the 'General Science
Journal'

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
 
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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.
 
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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