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Let $P$ be the prime zeta function $$ P (s) = \sum_{p\, \in\text{ primes}} \frac 1 {p^s} = \frac {1} {2^s} + \frac {1} {3^s} + \frac 1 {5^s} + \frac 1 {7^s} + \frac 1 {11^s} + \cdots $$ and define the ...

Consider the following prime sum: \begin{aligned} \sum _{p}{\frac {\cos(x\log p)}{p^{1/2}}} \end{aligned} whose spikes appear at the Riemann $\zeta$ zeros as shown here. Taking these detected spikes (...

I know the linked articles from Wikipedia for the Euler's totient function and the Dedekind psi function. I know that are in the literature famous, interesting and difficult problems involving the ...