An electro-mechanical investigation of the Riemann zeta function in the critical strip

@article{Pol1947AnEI,
  title={An electro-mechanical investigation of the Riemann zeta function in the critical strip},
  author={Balth. van der Pol},
  journal={Bulletin of the American Mathematical Society},
  year={1947},
  volume={53},
  pages={976-981}
}
  • B. V. D. Pol
  • Published 1 October 1947
  • Mathematics
  • Bulletin of the American Mathematical Society
View via Publisher
ams.org
19 Citations
Highly Influential Citations
2
Background Citations
4
Methods Citations
4

Figures from this paper

19 Citations

Fourier transforms related to ζ(s)

  • P. Panzone
  • Mathematics
    Proceedings of the Edinburgh Mathematical Society
  • 2021
Abstract Using some formulas of S. Ramanujan, we compute in closed form the Fourier transform of functions related to Riemann zeta function $\zeta (s)=\sum \nolimits _{n=1}^{\infty } {1}/{n^{s}}$ and…

Riemann zeros from a periodically-driven trapped ion

Ran He, Ming-Zhong Ai, Jin-Ming Cui1,2,∗ Yun-Feng Huang1,2,† Yong-Jian Han, Chuan-Feng Li1,2,‡ Guang-Can Guo, G. Sierra3,§ and C.E. Creffield4¶ CAS Key Laboratory of Quantum Information, University…

Riemann Zeroes from a Parametric Oscillator analyzed with Adiabatic Invariance, Hill Equation and the Least Action Principle

. Adiabatic Invariance (AdI), Hill´s Equation formalism (HEF), and the Least Action Principle (LAP), three relevant tools of theoretical physics are here separately applied to a one- dimensional…

Riemann zeros from Floquet engineering a trapped-ion qubit

The non-trivial zeros of the Riemann zeta function are central objects in number theory. In particular, they enable one to reproduce the prime numbers. They have also attracted the attention of…

Riemann zeros from Floquet engineering a trapped-ion qubit

The non-trivial zeros of the Riemann zeta function are central objects in number theory. In particular, they enable one to reproduce the prime numbers. They have also attracted the attention of…

Identifying the Riemann zeros by periodically driving a single qubit

The Riemann hypothesis, one of the most important open problems in pure mathematics, implies the most profound secret of prime numbers. One of the most interesting approaches to solve this hypothesis…

The Riemann Zeros as Spectrum and the Riemann Hypothesis

A spectral realization of the Riemann zeros based on the propagation of a massless Dirac fermion in a region of Rindler spacetime and under the action of delta function potentials localized on the square free integers suggests a proof of theRiemann hypothesis in the limit where the potentials vanish.

Will a physicist prove the Riemann hypothesis?

  • M. Wolf
  • Mathematics
    Reports on progress in physics. Physical Society
  • 2019
The Riemann Hypothesis is formulated and some physical problems related to this hypothesis are reviewed: the Polya--Hilbert conjecture, the links with Random Matrix Theory, relation with the Lee--Yang theorem on the zeros of the partition function and phase transitions, random walks, billiards etc.

A Fowler-Nordheim Integrator can Track the Density of Prime Numbers

It is reported for the first time that any hypothetical prime number generator, to the authors' knowledge, has to be a special case of a dynamical system that is governed by the physics of Fowler-Nordheim quantum-tunneling and how such a dynamicals system can be implemented using a counting process that naturally arises from sequential FN tunneling and integration of electrons on a floating-gate (FG) device.

Riemann zeros in radiation patterns: II. Fourier transforms of zeta

This extends a previous study (2012 J. Phys. A: Math. Theor. 45 302001) of two initial waveforms whose far-field radiation patterns possess sidelobes separated by the Riemann zeros. The analysis…