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 in form of a sum of series and integral representations 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 (i.e. Hermitian) dynamic potential operator enabled by an extended („exponential decay“) Hilbert space, which includes all distributional Sobolev type ("polynomial decay") 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, …

Some earlier related papers

Braun K., A Kummer function based Zeta function theory to prove the Riemann Hypothesis and the Goldbach conjecture, March 27, 2017

Braun K., A Kummer function based Zeta function theory to prove the Riemann Hypothesis and the binary Goldbach conjecture.pdf

Braun K., A distributional way to prove the Goldbach conjecture leveraging the circle method, Jan 8, 2015.pdf

 

Braun K., The Goldbach conjecture, a solution concept enabled by the alternative Zeta function theory

 

Braun K., A new integral and series representation of the Zeta function to prove the Riemann Hypothesis

 

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

 

Braun, K., The Kummer conjecture, p-th cyclotomic polynomials, the zeta function at odd integers, and all that ....pdf

                          

Braun K., Looking back, part A, (A1)-(A3)