A. Einstein, "We can't solve problems by using the same kind of thinking we used when we created them".
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.
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
by two independent random
variables, overcoming current challenges proving asymptotics of binary number