HIlbert-Polya conjecture proof of RH through Quantum mechanics

In summary, the conversation discusses the use of the Hamiltonian, Von Mangoldt formula, and WKB expansion to prove the Riemann Hypothesis through the Hilbert Polya conjecture. The proposed trace for exp(iuH) is the only possible one and the resulting nonlinear integral equation can be solved using numerical methods. However, the HP conjecture must first be proven and then it must be shown that it implies RH.
  • #1
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
 
Physics news on Phys.org
  • #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.
 
  • #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.
 

1. What is the Hilbert-Polya conjecture?

The Hilbert-Polya conjecture is a mathematical problem that was proposed by David Hilbert in 1900 and later revised by George Polya in the 1920s. It states that every non-negative integer can be expressed as a sum of squares of two integers.

2. How does the Hilbert-Polya conjecture relate to the Riemann Hypothesis?

The Hilbert-Polya conjecture is closely connected to the Riemann Hypothesis, which is one of the most famous unsolved problems in mathematics. The conjecture states that the distribution of prime numbers is closely related to the zeros of the Riemann zeta function.

3. What is the proposed proof of the Riemann Hypothesis through quantum mechanics?

The proposed proof of the Riemann Hypothesis through quantum mechanics is based on the idea that the Riemann zeta function can be expressed as a partition function of a quantum mechanical system. This approach was first proposed by physicist Freeman Dyson in the 1970s.

4. How does quantum mechanics play a role in this proof?

Quantum mechanics plays a crucial role in this proof by providing a mathematical framework to understand the behavior of the Riemann zeta function. The partition function of a quantum mechanical system is closely related to the Riemann zeta function, and by analyzing its properties, we can gain insights into the behavior of the zeta function.

5. Has the Riemann Hypothesis been proven through this approach?

No, the Riemann Hypothesis has not been proven through this approach yet. While there have been some promising developments and connections between quantum mechanics and the Riemann zeta function, a complete proof has not yet been achieved. This is still an active area of research and many mathematicians and physicists are working towards finding a proof through this approach.

Similar threads

On the origin and the evolution of information in the Universe
    • Cosmology
Replies
1
Views
1K
I Classical chaos and quantum mechanics
    • Quantum Physics
2
Replies
65
Views
7K
HIlbert-Polya conjecture ¿proof or RH?
    • Linear and Abstract Algebra
Replies
2
Views
10K
High Energy Recommended books in HEP, QFT, QM, GR
    • Science and Math Textbooks
Replies
9
Views
3K
Path integral Quantum Mechanics
    • Quantum Physics
Replies
15
Views
3K
Understanding the Hilbert Space Postulate in Quantum Mechanics?
    • Advanced Physics Homework Help
Replies
4
Views
2K
Quantum challenge: mathematical paradoxes
    • Quantum Physics
Replies
19
Views
3K
Quantum Mechanics: Normalization Requirements (E>Vmin)
    • Advanced Physics Homework Help
Replies
1
Views
5K
Recent papers on self-dual loop quantum black holes
    • Beyond the Standard Models
Replies
28
Views
4K
Exploring the Limits of Measurement in Quantum Mechanics
    • Quantum Physics
3
Replies
102
Views
16K

Hot Threads

Recent Insights

Back
Top