Gram's Law Fails a Positive Proportion of the Time

Abstract

This paper extends the work done by Titchmarsh on Gram's Law (an attempt to locate the zeroes of the zeta-function on the critical line). Herewith it is shown that a positive proportion of Gram intervals violate Gram's Law; and also that a weaker notion of Gram's Law is valid over a positive proportion of intervals.

arXiv comment10 pages