Will a physicist prove the Riemann Hypothesis?

Abstract

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 links with Random Matrix Theory, relation with the Lee--Yang theorem on the zeros of the partition function, random walks, billiards etc.

Many changes in this version. Hamiltonian for trivial zeros of zeta is proposed

References in corpus (19)

• Spatial variation in the fine-structure constant -- new results from VLT/UVES
• Physics of the Riemann Hypothesis
• Hamiltonian for the zeros of the Riemann zeta function
• Jensen polynomials for the Riemann zeta function and other sequences
• The ternary Goldbach conjecture is true
• Open circular billiards and the Riemann hypothesis
• The H=xp model revisited and the Riemann zeros
• The Quantum Mellin transform
• H = x p with interaction and the Riemann zeros
• Quantum mechanical potentials related to the prime numbers and Riemann zeros
• On some reasons for doubting the Riemann hypothesis
• Vacuum stability, string density of states and the Riemann zeta function
• Finding zeros of the Riemann zeta function by periodic driving of cold atoms
• Basic zeta functions and some applications in physics
• Survival Probability for Open Spherical Billiards
• Riemann hypothesis and Quantum Mechanics
• From Veneziano to Riemann: A String Theory Statement of the Riemann Hypothesis
• Equidistribution Rates, Closed String Amplitudes, and the Riemann Hypothesis
• On the Hamiltonian whose spectrum coincides with the set of primes

Cited by in corpus (13)

• Measure for chaotic scattering amplitudes
• Majorana quanta, string scattering, curved spacetimes and the Riemann Hypothesis
• Identifying primes from entanglement dynamics
• Randomness of Mobius coefficents and brownian motion: growth of the Mertens function and the Riemann Hypothesis
• Supersymmetric quantum mechanics and the Riemann hypothesis
• A Non-Linear Difference Equation for Calculation of the Zeros of the Riemann Zeta-Function on the Critical Line
• From the arrow of time in Badiali's quantum approach to the dynamic meaning of Riemann's hypothesis
• Numerical Simulation of GUE Two-Point Correlation and Cluster Functions
• The recurrence formulas for primes and non-trivial zeros of the Riemann zeta function
• A symmetry perspective of the Riemann zeros
• Using quantum computers to identify prime numbers via entanglement dynamics
• Equivalence between the zero distributions of the Riemann zeta function and a two-dimensional Ising model with randomly distributed competing interactions
• Quantum Physics, Algorithmic Information Theory and the Riemanns Hypothesis