Regarding the vonMongoldt formula:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\psi_0(x)=x-\sum_{\rho}\frac{x^{\rho}}{\rho}-ln(2\pi)-1/2ln(1-\frac{1}{x^2})[/tex]

I cannot understand why the sum over the complex zeros exhibits discontinuities at powers of primes. I understand why [itex]\psi_0(x)[/tex] does as this results from the derivation of the formula from a Mellin transform (Perron's formula) and a function derived from Chebyshev's function which itself is discontinuous at powers of primes. But why should the sum over the complex zeros exhibit the same type of discontinuity? They seem unrelated. I'll be looking into it. Might take a while though.

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# VonMangoldt formula

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