Caltech/UCLA Joint Analysis Seminar

Let S(t) = 1/(π Im log ζ(1/2+it)). The behavior of this function is intimately connected to irregularities in the locations of the zeros of the zeta function. In particular S(t) measures the difference between the "expected" number of zeta zeros up to height t and the actual number of such zeros. I will discuss what is known about the distribution of S(t) and prove a new unconditional lower bound on how often S(t) achieves large values.