Rainer Andreas Mittermeier

Understanding the Riemann Hypothesis: From the primes through Riemann's zeros and Suzuki's screw function to Mittermeier's prime-power checkpoints and the open infinite-tail problem

Suzuki's screw-function criterion makes the Riemann hypothesis equivalent to the pointwise nonnegativity of the real function Ψ = −gζ. The prime-power checkpoint approach developed here starts from this equivalence and identifies an exact geometric structure in Ψ. The curvature o...

Prime-power checkpoints for the Riemann zeta screw function: Plastic-Constant Convexity and a Restricted Legendre--Mangoldt Representation

Masatoshi Suzuki's Riemann-zeta screw function g_zeta has the associated real positivity function Psi = -g_zeta, and his pointwise criterion makes the Riemann hypothesis equivalent to Psi(t) >= 0 for every real t. We show that after the first arithmetic event its smooth reservoir...

The Remaining Riemann-Hypothesis Tail: From Prime-Power Checkpoints to Smoothed von Mangoldt Bounds

For Suzuki's Riemann-zeta screw function g_zeta, the associated real function Psi = -g_zeta satisfies RH if and only if Psi(t) >= 0 for every real t. A prime-power checkpoint theorem reduces the positive half-line to one constrained minimum between consecutive prime powers, and d...

Prime-power checkpoints for the Riemann zeta screw function: Plastic-Constant Convexity and a Restricted Legendre--Mangoldt Representation

Masatoshi Suzuki's Riemann-zeta screw function g_zeta has the associated real positivity function Psi = -g_zeta, and his pointwise criterion makes the Riemann hypothesis equivalent to Psi(t) >= 0 for every real t. We show that after the first arithmetic event its smooth reservoir...

Prime-Power Checkpoints for Suzuki's Riemann Zeta Screw Function: Rigorous Positivity Certificate through q = 10^10 and an Explicit Chebyshev-Memory Barrier

The prime-power checkpoint theorem reduces the pointwise Riemann-hypothesis criterion associated with Suzuki's screw function g_zeta to complete interval minima of Psi = -g_zeta. We implement that reduction as a streaming directed-rounding certificate and close all 455,062,595 pr...

Prime-power checkpoints for the Riemann zeta screw function: Plastic-Constant Convexity and a Restricted Legendre--Mangoldt Representation

Building on Suzuki's pointwise criterion for the Riemann hypothesis, this paper reduces its continuous sign condition to one uniquely determined checkpoint on each interval between consecutive prime powers. The key geometric input is an exact factorization of the smooth archimede...