On Propositions Pertaining to the Riemann Hypothesis IV

In this paper, we enumerate certain hypotheses regarding the Riemann zeta function. The hypotheses are in the form of bounds on the norm of the tail of the sequence that determines the Riemann zeta function and also an optimization problem involving Diophantine approximation. These are related to Ω-phenomena, arising infinitely often along the imaginary axis, such as concentration phenomena. We also relate these hypotheses with the Riemann and Lindelof hypotheses.