About this strategy to prove Riemann Hypothesis

In summary, the conversation discusses the definition of two operators, D_{+} and D_{-}, which satisfy certain properties. The Hamiltonian, H, is then defined in terms of these operators and is shown to be Hermitian. The energies, E_{n}, are related to the zeros of the Riemann zeta function. The conversation also questions whether the author has proven the Riemann Hypothesis and discusses the validity of his claims.
  • #1
zetafunction
391
0
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 [tex] D_{+} [/tex] and [tex] D_{-} [/tex] so they satisfy the properties [tex] D_{+} = D^{*}_{-} [/tex] [tex] D_{-} = D^{*}_{+} [/tex]

[tex] D_{+} =x\frac{d}{dx}+ \frac{dV}{dx} [/tex]

[tex] D_{-} =-x\frac{d}{dx}+ \frac{dV}{dx} [/tex]

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

and the energies would be [tex] E_{n}= s_{n} (1-s_{n}) [/tex] , 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 ?
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
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.
 
  • #3
it is simply operator theory ,

although i believe that if s is an eigenvalue of [tex] D_{+} [/tex] , then the complex conjugate to 's' will be the eigenvalue of [tex] D_{-} [/tex] , so the Eigenvalues of Hamiltonian H will be [tex] H\Psi = s.s^{*}\Psi [/tex] , so perhaps we will need another condition
 
  • #4
zetafunction said:
have this man proved Riemann HYpothesis ?

No .
 
  • #5
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.
 
  • #6
0102031v10.pdf this is version ten of the paper ... ?
 

Related to About this strategy to prove Riemann Hypothesis

1. What is the Riemann Hypothesis?

The Riemann Hypothesis is a famous unsolved problem in mathematics that was proposed by German mathematician Bernhard Riemann in 1859. It states that all non-trivial zeros of the Riemann zeta function lie on the critical line, which is a vertical line in the complex plane where the real part of the zeta function is equal to 1/2. This hypothesis has far-reaching consequences in number theory and has remained unproven for over 160 years.

2. Why is it important to prove the Riemann Hypothesis?

The Riemann Hypothesis is one of the most important unsolved problems in mathematics. It has connections to many other areas of mathematics, such as prime number theory, algebraic geometry, and harmonic analysis. If proven, it would provide deep insights into the distribution of prime numbers and would have significant implications for theorems and conjectures in these other fields.

3. What are some current strategies to prove the Riemann Hypothesis?

There are several different approaches that mathematicians have taken to try and prove the Riemann Hypothesis. Some of these include using analytical methods, such as the Hardy-Littlewood conjectures, and algebraic methods, such as the Langlands program. Other strategies involve using connections to other unsolved problems in mathematics, such as the Birch and Swinnerton-Dyer conjecture.

4. Why has the Riemann Hypothesis been so difficult to prove?

The Riemann Hypothesis has been notoriously difficult to prove because it involves complex mathematical concepts and requires deep insights and techniques from multiple areas of mathematics. Additionally, the hypothesis has been tested extensively and has held true for the first trillions of zeros of the zeta function, making it seem very likely to be true. However, there is still no proof, and it remains a challenging and open problem in mathematics.

5. What are some potential implications if the Riemann Hypothesis is proven?

If the Riemann Hypothesis is proven, it would have significant implications in the world of mathematics. It would provide a better understanding of the distribution of prime numbers and could potentially lead to the proof of other important conjectures and theorems. It would also have practical applications in fields such as cryptography and computer science, where prime numbers play a crucial role.

Similar threads

B Does this help solve the Riemann Hypothesis?
    • General Math
Replies
4
Views
1K
I A thought about the Riemann hypothesis
    • General Math
Replies
7
Views
1K
Exploring the Riemann Hypothesis and Analytic Continuation
    • Linear and Abstract Algebra
Replies
2
Views
4K
MHB Euler/Riemann Point of Departure in Riemann's 1859 paper containing RH
    • General Math
Replies
1
Views
1K
A proposed Hamiltonian operator for Riemann Hypothesis
    • Linear and Abstract Algebra
Replies
32
Views
9K
The clue to the proof of Riemann hypothesis
    • Linear and Abstract Algebra
Replies
4
Views
2K
Understanding the Zeta Function and Riemann Hypothesis: A Beginner's Guide
    • Linear and Abstract Algebra
Replies
8
Views
10K
Programming details on the computation of the Riemann zeta function using Aribas
    • Linear and Abstract Algebra
Replies
4
Views
5K
Riemann Hypothesis: Question on Critical Line
    • Linear and Abstract Algebra
Replies
2
Views
3K
Is the Riemann Hypothesis Finally Proven?
    • Linear and Abstract Algebra
Replies
4
Views
3K

Hot Threads

Recent Insights

Back
Top