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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 |
