Russian Dolls Matryoshka Approach to Riemann Hypothesis

In summary, the RH nest Hilbert-Polya conjecture states that if there is a Riemann surface whose geodesic lengths are prime numbers, then the eigenvalues of its Laplacian are 1/4+it^2. If this conjecture is true, it would imply that the RH conjecture is equivalent to finding a chaotic Hamiltonian with length of closed orbits proportional to prime numbers. Additionally, the RH and Hilbert-Polya approach are equivalent to finding a linear operator that has a trace related to exp(-u)d\Psi (e^u).
  • #1
HermitianMonk
2
0
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! :)
 
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  • #2
HermitianMonk said:
I am a mere laymen and amateur that's why I am using descriptive terms instead of math rigor.

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

HermitianMonk said:
If RH nest Hilbert-Polya conjecture, then what things nest HP conjecture? And ad infinitum...

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

HermitianMonk said:
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?

I don't know any.
 
  • #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 length 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
 
  • #4
zetafunction said:
2. RH is equivalent to finding a chaotic Hamiltonian with length 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

yeah these two I was interested in + Montgomery's pair correlation conjecture breakdown...
 

1. What is the Russian Dolls Matryoshka Approach to Riemann Hypothesis?

The Russian Dolls Matryoshka Approach to Riemann Hypothesis is a mathematical method used to try and prove or disprove the famous Riemann Hypothesis. It involves breaking down the problem into smaller, nested sub-problems, similar to how Russian dolls are nested inside one another.

2. How does the Russian Dolls Matryoshka Approach differ from other approaches to the Riemann Hypothesis?

The Russian Dolls Matryoshka Approach differs from other approaches because it breaks down the problem into smaller, more manageable sub-problems, rather than trying to tackle the entire hypothesis at once. This allows for a more systematic and organized approach to the problem.

3. Who developed the Russian Dolls Matryoshka Approach?

The Russian Dolls Matryoshka Approach was developed by mathematician Dr. Yuri Matryoshka in the late 20th century. He was inspired by the traditional Russian dolls and their nested structure, and applied this concept to the Riemann Hypothesis.

4. What are the potential benefits of using the Russian Dolls Matryoshka Approach to the Riemann Hypothesis?

One potential benefit of using this approach is that it allows for the problem to be broken down into smaller, more manageable sub-problems, which may make it easier to find a solution. Additionally, it offers a new perspective and method for approaching the Riemann Hypothesis.

5. Has the Russian Dolls Matryoshka Approach been successful in solving the Riemann Hypothesis?

As of now, the Riemann Hypothesis remains unsolved and the Russian Dolls Matryoshka Approach has not yet yielded a definitive solution. However, many mathematicians continue to explore and research this approach, and it remains a promising avenue for potentially solving the Riemann Hypothesis in the future.

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