HIlbert-Polya conjecture proof of RH through Quantum mechanics

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SUMMARY

The discussion centers on proving the Riemann Hypothesis (RH) through the Hilbert-Polya conjecture by identifying a Hamiltonian, specifically H=p²V(x), where the energies correspond to the imaginary parts of the non-trivial zeros of the Riemann zeta function. The use of the Von Mangoldt formula for the Chebyshev function and the WKB expansion leads to an integral equation for V(x). The proposed trace for exp(iuH) is deemed the only viable option if the Von Mangoldt formula is accepted as correct. However, two significant hurdles remain: proving the Hilbert-Polya conjecture and demonstrating its implication for RH.

PREREQUISITES
  • Understanding of Quantum Mechanics, specifically Hamiltonians
  • Familiarity with the Von Mangoldt formula and Chebyshev functions
  • Knowledge of WKB expansion techniques
  • Basic concepts of the Riemann Hypothesis and its significance in mathematics
NEXT STEPS
  • Research Hamiltonians in Quantum Mechanics and their applications
  • Study the Von Mangoldt formula and its implications for number theory
  • Explore WKB approximation methods in quantum mechanics
  • Investigate the relationship between the Hilbert-Polya conjecture and the Riemann Hypothesis
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Mathematicians, physicists, and researchers interested in number theory, quantum mechanics, and the Riemann Hypothesis, particularly those exploring advanced mathematical proofs and conjectures.

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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