About this strategy to prove Riemann Hypothesis

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Discussion Overview

The discussion revolves around a proposed strategy to prove the Riemann Hypothesis using operator theory, specifically through the definition of two operators, D_{+} and D_{-}, and their relationship to a Hamiltonian. Participants explore the implications of this approach and express varying opinions on its validity and complexity.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant shares a paper that defines operators D_{+} and D_{-} and suggests that their properties could lead to a proof of the Riemann Hypothesis.
  • Another participant critiques the use of "Hamiltonian" and "energy" terminology in a mathematical context, suggesting it complicates the discussion.
  • It is proposed that if 's' is an eigenvalue of D_{+}, then its complex conjugate would be the eigenvalue of D_{-}, indicating a potential need for additional conditions for the Hamiltonian's eigenvalues.
  • A participant explicitly states that the author of the paper has not proved the Riemann Hypothesis.
  • One participant expresses skepticism about the author, labeling them as a "crackpot" and questioning their academic credentials and claims regarding other theories.
  • There is a question about the versioning of the paper mentioned, indicating an interest in the evolution of the author's work.

Areas of Agreement / Disagreement

Participants express disagreement regarding the validity and clarity of the proposed strategy, with some supporting the exploration of operator theory while others criticize its complexity and the author's credibility. The question of whether the Riemann Hypothesis has been proved remains unresolved.

Contextual Notes

Participants note the potential complexity and vagueness introduced by the terminology used in the paper, as well as the need for additional conditions related to the eigenvalues of the Hamiltonian.

zetafunction
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http://arxiv1.library.cornell.edu/PS_cache/math/pdf/0102/0102031v10.pdf and http://arxiv1.library.cornell.edu/PS_cache/math/pdf/0102/0102031v1.pdf

what do you think ?

Author defines 2 operators D_{+} and D_{-} so they satisfy the properties D_{+} = D^{*}_{-} D_{-} = D^{*}_{+}

D_{+} =x\frac{d}{dx}+ \frac{dV}{dx}

D_{-} =-x\frac{d}{dx}+ \frac{dV}{dx}

If we define the Hamiltonian H= D_{+}D_{-} this Hamiltonian would be Hermitian

and the energies would be E_{n}= s_{n} (1-s_{n}) , here 's' are the zeros for the Riemann zeta function , so since the eigenvalues are real s(1-s) is real ONLY whenever ALL the zeros have real part 1/2 but ¿is this true ? , have this man proved Riemann HYpothesis ?
 
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Talking about the "Hamiltonian" and "energy" for a purely mathematics problem looks to me as just a way of making things more complicated and vaguer.
 
it is simply operator theory ,

although i believe that if s is an eigenvalue of D_{+} , then the complex conjugate to 's' will be the eigenvalue of D_{-} , so the Eigenvalues of Hamiltonian H will be H\Psi = s.s^{*}\Psi , so perhaps we will need another condition
 
zetafunction said:
have this man proved Riemann HYpothesis ?

No .
 
It amuses me to research these crackpots. Besides proving the Riemann Hypothesis, he has also generalized General Relativity, Super String Theories, Quantum Mechanics and every other physical theory into "Topological GeometroDynamics (TGD)". He fraudulently states he is a Professor at the University of Helsinki, and provides false links to his non-existent University webpage to boot.
 
0102031v10.pdf this is version ten of the paper ... ?
 

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