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The Theory of Hardy’s Z-Function by Aleksandar Ivi

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11

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 images 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 ...

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