On Propositions Pertaining to the Riemann Hypothesis IV
Pathikrit Basu *
MSQE, Indian Statistical Institute, New Delhi, India and 20128 White Cloud Circle, West Linn, Oregon-9706. USA.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Riemann hypothesis, r iemann zeta function, lindelof hypothesis, probability measures over the unit circle, Ω-phenomena