On Propositions Pertaining to the Riemann Hypothesis III

Abstract

In this paper, we consider further propositions concerning the range of possible distributions over the unit circle, for the Riemann zeta function as in prior research. We also derive some new upper bounds on the sum of norms for the tail sequence corresponding to the Riemann zeta function. We discuss some hypotheses, conditional on which, properties of concentrated distributions may be obtained. Specific sub-classes are shown of distributions that occur infinitely often along the imaginary axis.