On some problems involving Hardy’s function and zeta-moments
11.1 The distribution of values of Hardy’s function
This last chapter is devoted to some open problems involving Hardy’s function and zeta-moments. It is hoped that this will be of interest to all who want to do research in areas connected to these topics. The aim of this section is to study the distribution of positive and negative values of Z(t). This is an important problem, since Z(t) is a highly oscillating function, with T log T zeros in [0, T] (see (1.49). Also recall that (see (1.53)
so that takes some fairly large values.
To study the distribution of values of Z(t) we ...