# Random matrices, generalized zeta functions and self-similarity of zero distributions

@article{Shanker2006RandomMG, title={Random matrices, generalized zeta functions and self-similarity of zero distributions}, author={O. Shanker}, journal={Journal of Physics A}, year={2006}, volume={39}, pages={13983-13997} }

There is growing evidence for a connection between random matrix theories used in physics and the theory of the Riemann zeta function and L-functions. The theory underlying the location of the zeros of these generalized zeta functions is one of the key unsolved problems. Physicists are interested because of the Hilbert–Polya conjecture, that the non-trivial zeros of the zeta function correspond to the eigenvalues of some positive operator. To complement the continuing theoretical work, it would…

## 15 Citations

Rescaled Range Analysis of L-function zeros and Prime Number distribution

- Mathematics
- 2008

The statistical properties of the distribution of zeros of the Riemann zeta function and related functions are of interest in mathematics and physics. We apply the tool of rescaled range analysis to…

An open letter concerning Explanation of low Hurst exponent for Riemann zeta zeros

- Philosophy
- 2011

In 2006 a striking result was published (Generalised Zeta Functions and Self-Similarity of Zero Distributions, J. Phys. A 39(2006), 13983-13997) about the statistics of the zeros of the Riemann zeta…

Entropy of Riemann zeta zero sequence

- Computer Science
- 2013

The entropy of the sequence of zeros is studied, which tells us how constrained is the pattern ofZeros, and a low value would give encouragement that techniques in machine learning like neural networks would be helpful in studying the phenomenon.

Neural Network prediction of Riemann zeta zeros

- Computer Science
- 2012

Neural network regression is applied as a tool to aid the empirical studies of the locations of the zeros in the Riemann Zeta Function using values evaluated at the Gram points as the input feature set for predictions.

Good-to-Bad Gram Point Ratio for Riemann Zeta Function

- MathematicsExp. Math.
- 2021

The formulation and experimental validation of two symmetry-related conjectures about the location of the zeros of the Riemann zeta function are presented and two new results are presented.

Colloquium: Physics of the Riemann hypothesis

- Physics
- 2011

Physicists become acquainted with special functions early in their studies. Consider our perennial model, the harmonic oscillator, for which we need Hermite functions, or the Laguerre functions in…

Numerical information processing under the global rule expressed by the Euler-Riemann ζ function defined in the complex plane.

- MathematicsChaos
- 2010

A fresh look at the triple (η,ζ,λ) is presented which suggests an elementary analysis based on the distances of the three complex numbers z, z/2, and 2/z to 0 and 1 and shed new epistemological light about the critical line.

Scale-invariant correlations and the distribution of prime numbers

- Mathematics, Psychology
- 2009

Negative correlations in the distribution of prime numbers are found to display a scale invariance. This occurs in conjunction with a nonstationary behavior. We compare the prime number series to a…

Correlations in Prime Number Distribution and L-function Zeros

- Mathematics
- 2009

A simple analysis of the gaps in primes shows an interesting correlation between neighbouring primes. Neighbouring primes are more likely to have difiering remainders on being divided by 6 (the…

RANDOM WALK IN SHORTCUT MODELS

- Mathematics
- 2008

Earlier studies of a parametrized class of models whose fractal dimension transitions from one to two indicated that the transition occurs infinitely sharply at the parameter value p=0, as the system…

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