RH, Goldbach, Euler
Unified Field Theory
UFT & MHD
UFT & HD
History
Literature
Who I am



A. Einstein, "We can't solve problems by using the same kind of thinking we used when we created them".

Based on the negative real zeros of the Digamma function an alternative representation of the Riemann density function J(x) is provided where its critical (oscillating) sum is replaced by two non-oscillating sums, both enjoying the required asymptotics O(square root of x), which proves the Riemann Hypothesis.

The specific common properties of the real negative zeros of the Digamma function and the imaginary part of the only complex valued zeros of a specific Kummer function allow the definition of corresponding weighted „retarding“ sequences fulfilling the Kadec condition. This enables the full power of non-harmonic Fourier series theory on the periodic L(2) Hilbert space with its relation to the Paley-Wiener space. In line with the proof of the RH those sequences allow a split of the Riemann density function J(x) into a sum of two number theoretical non-harmonic Fourier series, each of them governing one of two unit half-circles. Those two independent distribution functions can be applied to pick pairs of primes by two independent random variables, overcoming current challenges proving asymptotics of binary number problems.

    

Braun K., A Digamma function based proof of the RH and a nonharmonic Fourier series based two-semi-circle method to solve additive number theory problems


                                             August 25, 2021
                                         

    

Braun K., A Bessel function based proof that the Euler constant is irrational


                                             December 2, 2021


Supporting papers

   

Braun K., Supporting data to prove the RH and the Goldbach conjecture


                                            August 26, 2021

                         

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


                                             April 18, 2021

                                       

Braun K., RH solutions


                                              July 31, 2019


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


                                          March 27, 2017
                         
                                 

Braun K., A distributional way to prove the Goldbach conjecture leveraging the circle method


                                            Jan 8, 2015              


Further supporting data

                           

Edwards H. M., Riemann s Zeta Function


                       

(LeB) Lectures on Entire Functions, Lecture 5


                       

(LeN) Gap and density theorems, VI and VII


            

(PaR) Fourier transforms in the complex domain, 22 and 33


                  

Wiener N., The mean square modulus of a function