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 ?