# How does one prove Riemann's explicit formula?

Q: Is there a reference for a detailed proof of Riemann's explicit formula ?

I am reading the TeXified version of Riemann's manuscript, but sometimes I can't follow (I think the author has kept typos from the orignal paper).

Here are some points I have trouble with (but there are others) :

• How does he calculate $$\int_{a+i\mathbb{R}} \frac{d}{ds} \left( \frac{1}{s} \log(1-s/\beta)\right) x^s ds$$ on page 4 ?

• What do I need to know about $Li(x)$ to see how the terms $Li(x^{1/2+i\alpha})$ appear ?

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About the $\mathrm{Li}$ function you probably won't need more than Wikipedia's informations.