The relationship between Z and PZ can be established using:

PZ(s) = sum {k=1,∞} µ(k) * log(Z(k*s))/k

In the attached chart, it shows how close are Z and exp(PZ) for s>2.

In 2017, I introduced an approximation CZeta(s) for Z(s) in the form:

CZ(s) = 1 / ( 1 -π^-s - 2^-s)

the chart shows how CZ approaches Z and e^PZ for values s>2.

The Im(s) for the zeros of PZ less than 1000 is π/2

The trend line for the logarithms of zeta at the non-trivial zeros.

Full chart of the first 1000 zeros of PZ

Zeros of PZ with Re(s)<3

Zeros of PZ with Re(s)<3 and Im(s)<800.

When representing Im(s) vs. Re(s) for s=zero of PZ, four clusters emerge.

Im(log(s)) vs. Re(log(s))

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