## 26 Citations

### ON STRATEGIES TOWARDS THE RIEMANN HYPOTHESIS: FRACTAL SUPERSYMMETRIC QM AND A TRACE FORMULA

- Mathematics
- 2007

The Riemann hypothesis (RH) states that the non-trivial zeros of the Riemann zeta-function are of the form sn = 1/2+iλn. An improvement of our previous construction to prove the RH is presented by…

### A Fractal Susy-Qm Model and the Riemann Hypothesis

- Mathematics
- 2003

The Riemann’s hypothesis (RH) states that the nontrivial zeros of the Riemann zeta-function are of the form s = 1/2+iλn. Hilbert-Polya argued that if a Hermitian operator exists whose eigenvalues are…

### Fractal Supersymmetric Qm, Geometric Probability and the Riemann Hypothesis

- Mathematics
- 2004

The Riemann's hypothesis (RH) states that the nontrivial zeros of the Riemann zeta-function are of the form sn=1/2+iλn. Earlier work on the RH based on supersymmetric QM, whose potential was related…

### Riemann hypothesis and super-conformal invariance

- Mathematics
- 2001

A strategy for proving (not a proof of, as was the first over-optimistic belief) the Riemann hypothesis is suggested. The vanishing of Riemann Zeta reduces to an orthogonality condition for the…

### ON THE RIEMANN HYPOTHESIS AND TACHYONS IN DUAL STRING SCATTERING AMPLITUDES

- Mathematics
- 2006

It is the purpose of this work to pursue a novel physical interpretation of the nontrivial Riemann zeta zeros and prove why the location of these zeros zn = 1/2+iλn corresponds physically to…

### On SUSY-QM, fractal strings and steps towards a proof of the Riemann hypothesis

- Mathematics
- 2001

We present, using spectral analysis, a possible way to prove the Riemann's hypothesis (RH) that the only zeroes of the Riemann zeta-function are of the form s=1/2+i\lambda_n. A supersymmetric quantum…

### The Riemann zeros and the cyclic renormalization group

- Physics
- 2005

We propose a consistent quantization of the Berry–Keating Hamiltonian xp, which is currently discussed in connection with the non-trivial zeros of the Riemann zeta function. The smooth part of the…

### The Riemann Hypothesis is a Consequence of CT-Invariant Quantum Mechanics

- Mathematics
- 2009

The Riemann's hypothesis (RH) states that the nontrivial zeros of the Riemann zeta-function are of the form sn = 1/2 + iλn. By constructing a continuous family of scaling-like operators involving the…

### Symmetry argument for the Riemann hypothesis , universality & broken symmetry

- Physics
- 2007

Upon careful re-examination of Riemann’s original work in the analytic continuation of the function ( ) s ς throughout the complex plane in general, and across the critical strip in particular, a…

### Quantization of the Riemann Zeta-Function and Cosmology

- Mathematics
- 2007

Quantization of the Riemann zeta-function is proposed. We treat the Riemann zeta-function as a symbol of a pseudodifferential operator and study the corresponding classical and quantum field…

## References

SHOWING 1-10 OF 49 REFERENCES

### The Riemann Zeros and Eigenvalue Asymptotics

- MathematicsSIAM Rev.
- 1999

It is speculated that the Riemann dynamics is related to the trajectories generated by the classical hamiltonian Hcl=XP, and very refined features of the statistics of the tn can be computed accurately from formulae with quantum analogues.

### Topological geometrodynamics

- Physics
- 1983

An elementary particle model is proposed drawn from the string model and Yang-Mills theory. Instead of describing a particle as a mathematical point, we identify it as three-dimensional submanifold…

### SUPERCOMPUTERS AND THE RIEMANN ZETA FUNCTION

- Computer Science
- 1989

A new algorithm, invented by the speaker and A. Scho .

### Proof of Riemann hypothesis

- Mathematics
- 2001

Riemann hypothesis is proven by reducing the vanishing of Riemann Zeta function to an orthogonality condition for eigenfunctions of a generalized Hilbert-Polya operator having the zeros of the…

### Supersymmetry in Disorder and Chaos

- Physics
- 1996

1. Introduction 2. Supermathematics 3. Diffusion modes 4. Nonlinear supermatrix sigma- model 5. Perturbation theory and renormalization group 6. Energy level statistics 7. Quantum size effects in…