# Will a physicist prove the Riemann hypothesis?

@article{Wolf2014WillAP, title={Will a physicist prove the Riemann hypothesis?}, author={Marek Wolf}, journal={Reports on Progress in Physics}, year={2014}, volume={83} }

In the first part we present the number theoretical properties of the Riemann zeta function and formulate the Riemann hypothesis. In the second part we review some physical problems related to this hypothesis: 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.

## 24 Citations

### The Riemann Zeros as Spectrum and the Riemann Hypothesis

- 2019

Mathematics

Symmetry

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.

### Almost all of the nontrivial zeros of the Riemann zeta-function are on the critical line

- 2022

Mathematics, Philosophy

Applying Littlewood’s lemma in connection to Riemann’s Hypothesis and exploiting the symmetry of Riemann’s xi function we show that almost all nontrivial Riemann’s Zeta zeros are on the critical line.

### Supersymmetric quantum mechanics and the Riemann hypothesis

- 2022

Physics

We construct a supersymmetric quantum mechanical model in which the energy eigenvalues of the Hamiltonians are the products of Riemann zeta functions. We show that the trivial and nontrivial zeros of…

### Quantum Physics, Algorithmic Information Theory and the Riemanns Hypothesis

- 2017

Mathematics

In the present work the Riemanns hypothesis (RH) is discussed from four different perspectives. In the first case, coherent states and the Stengers approximation to Riemann-zeta function are used to…

### The Disproof of the Riemann Hypothesis

- 2021

Mathematics, Philosophy

We show that there is a contradiction between the Riemann’s Hypothesis and some form of the theorem on the universality of the zeta function.

### The Proof of the Riemann Hypothesis on a Relativistic Turing Machine

- 2017

Mathematics

In this article, the proof of the Riemann hypothesis is considered using the calculation of the Riemann ζ-function on a relativistic computer. The work lies at the junction of the direction known as…

### The Riemann Hypothesis is not true

- 2021

Philosophy, Mathematics

We show that there is a contradiction between the Riemann’s Hypothesis and the theorem on the strong universality of the zeta function

### Supersymmetric quantum mechanical system for locating the Riemann zeros

- 2023

Physics

The European Physical Journal Plus

The ground-state energy of a supersymmetric quantum mechanical system naturally vanishes. We use this important property of the supersymmetric system to study the location of zeros of the Riemann…

### Majorana quanta, string scattering, curved spacetimes and the Riemann Hypothesis

- 2021

Mathematics

Physica Scripta

The Riemann Hypothesis states that the Riemann zeta function ζ(z) admits a set of ‘non-trivial’ zeros that are complex numbers supposed to have real part 1/2. Their distribution on the complex plane…

### A Non-Linear Difference Equation for Calculation of the Zeros of the Riemann Zeta-Function on the Critical Line

- 2018

Mathematics

In this work, we present a non-linear difference equation for calculation of the zeros of the Riemann's zeta-function on the critical line. Our proposed non-linear map uses the Lambert W function and…

## 163 References

### Lorentz-invariant Hamiltonian and Riemann hypothesis

- 1998

Mathematics

We have given some arguments that a two-dimensional Lorentz-invariant Hamiltonian may be relevant to the Riemann hypothesis concerning zero points of the Riemann zeta function. Some eigenfunction of…

### The Number-Theoretical Spin Chain and the Riemann Zeroes

- 1998

Mathematics

Abstract:It is an empirical observation that the Riemann zeta function can be well approximated in its critical strip using the Number-Theoretical Spin Chain. A proof of this would imply the Riemann…

### Trace formula in noncommutative geometry and the zeros of the Riemann zeta function

- 1997

Mathematics

Abstract. We give a spectral interpretation of the critical zeros of the Riemann zeta function as an absorption spectrum, while eventual noncritical zeros appear as resonances. We give a geometric…

### From Veneziano to Riemann: A String Theory Statement of the Riemann Hypothesis

- 2015

Mathematics

We discuss a precise relation between the Veneziano amplitude of string theory, rewritten in terms of ratios of the Riemann zeta function, and two elementary criteria for the Riemann hypothesis…

### A conjecture for the sixth power moment of the Riemann zeta-function

- 1998

Mathematics

The authors conjecture an asymptotic expression for the sixth power moment of the Riemann zeta function. They establish related results on the asymptotics of the zeta function that support the…

### The Theory of the Riemann Zeta-Function

- 1987

Mathematics

The Riemann zeta-function embodies both additive and multiplicative structures in a single function, making it our most important tool in the study of prime numbers. This volume studies all aspects…

### On some reasons for doubting the Riemann hypothesis

- 2003

Mathematics

Several arguments against the truth of the Riemann hypothesis are extensively discussed. These include the Lehmer phenomenon, the Davenport-Heilbronn zeta-function, large and mean values of…

### High moments of the Riemann zeta-function

- 1999

Mathematics

The authors describe a general approach which, in principal, should produce the correct (conjectural) formula for every even integer moment of the Riemann zeta function. They carry it out for the…

### Statistical Theory of Numbers

- 1990

Physics

This article is three-sided: it is a pedestrian introduction to the Riemann hypothesis in the case of the classical zeta function, it provides also an elementary presentation of Quantum Statistical…

### The Positivity of a Sequence of Numbers and the Riemann Hypothesis

- 1997

Mathematics

Abstract In this note, we prove that the Riemann hypothesis for the Dedekind zeta function is equivalent to the nonnegativity of a sequence of real numbers.