A short proof of the RH is provided. It is enabled by a combined integral AND series representation of Riemann’s meromorph Zeta function occuring in the symmetrical form of his functional equation, (EdH) 1.6, 1.7. This representation is a simple application of one of Milgram's integral and series representations, (MiM).

There are basically two conceptual touchpoints between the RH and the scope of the UFT. Those are
         
-  the (statistical) Montgomery-Odlyzko law         
-  the Berry-Keating (Hilbert-Polya) conjecture
 
 Accordingly, the technical relations to the proposed UFT are
 
 - the compact embeddingness of the (thermo-) statistical Hilbert space L(2) into H(-1/2); the latter distributional Hilbert space is the dual Hilbert space of the newly proposed dynamic energy Hilbert space H(1/2) solving the 3D-NSE problem

 - the Krein space intrinsic self-adjoint potential operator of the proposed extended („exponential decay“) Hilbert space including all ("polynomial decay") distributional (Sobolev type) Hilbert spaces. It turned out that this („exponential decay“) Hilbert space provides the appropriate domain for hyperbolic PDE (e.g., wave and radiation equations.

                     

Braun K., A proof of the Riemann Hypothesis.pdf

                                                August 2023

 

Braun K., A simple Dirichlet series based proof of the Riemann Hypothesis?.pdf

                                             December 2024

                                               Main references

   

Braun K., A toolbox to build a non-harmonic Fourier series based two-semicircle method.pdf

 

Braun K., The Montgomery-Odlyzko law, eigenvalue spacing in a collection of Gaussian unitary operators

                             

Edwards H. M., Riemann s Zeta Function

(MiM) Milgram M. S., Integral and Series Representations of Riemann’s Zeta Function, …