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January 7[edit]

Reimann's jump[edit]

Hello, I'm currently working through the below famous paper;

http://www.scribd.com/doc/7631989/On-the-Number-of-Prime-Numbers-Less-Than-a-Given-Quantity

I understand fully until the final line on the bottom of page 2 at which point the proof seems to take a completely different and difficult to understand turn. Can someone please help me here? — Preceding unsigned comment added by 86.169.46.80 (talk) 20:31, 7 January 2014 (UTC)[reply]

I'm not an expert in this material. Riemann doesn't seem to define the function Π, but comparison with Riemann zeta function suggests that Π(s - 1) = Γ(s)? So, to tackle your problem at the bottom of page 2, try studying the properties of the gamma function? Mgnbar (talk) 19:27, 12 January 2014 (UTC)[reply]

The Π notation isn't as well known but is still standard notation for Γ shifted to coincide with factorial. The paper does tend to skip a lot of steps. There is a series of videos (mentioned previously on this page) from Mr. You Math on the zeta function which covers much of the same material but in much smaller increments, so it might be better to view them before tackling the source. --RDBury (talk) 08:17, 13 January 2014 (UTC)[reply]

I appreciate this but I understand the pi function and I was the one who posted the videos on here. But unfortunately Mr You Math stopped at the top of page 1 of the paper. I just don't understand how he makes this jump to this random equation at the bottom of page 2 from the line before it.