It is shown explicitly how the sign of Hardy's function $Z(t)$ depends on the parity of the zero-counting function $N(T)$. Two existing definitions of this function are analyzed, and some related problems are discussed.
A note on the zeros of the derivatives of Hardy's function $Z(t)$
Hardy's function $Z(t)$ - results and problems
On the derivatives of Hardy's function $Z(t)$
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