This post serves only one purpose: a place for me to keep links, and reveal my (lack of) knowledge on this subject. If you can help, feel free to leave a comment…

I wanted to see if the “Riemann hypothesis” could mean more to me than “an unsolved mathematical puzzle.” (Some may say this is not a proper entry in the “Comp. Sci.” category, but I’m interested in the opportunity to hone/refresh my math skills.)

**Background: **A good explanation is at the Physics Forums, under number theory: “Riemann Zeta Function?” It’s the first I found, with a link to *another, better discussion*, where some more elaboration is given — also a link to American Scientist article on the subject (an interesting read itself — giving some of the relationships to various applications).

*In short, from the above paragraph:* Riemann extended the Euler summation function (equiv. to the Euler product) using *analytic continuation* to the zeta function for all values (since Euler’s sum only converges for values greater than 1).

Less helpful by itself, but good reference, also giving related functions, and a couple of nice graphs, is the Wolfram Mathworld entry on the Riemann hypothesis.

**Current State: **It’s clear that, almost by defn. the equation on page two of this AMS article is equivalent to eq. 13 and 14 of the MathWorld entry;

I am trying to figure out if the equation in the fourth post of the *2nd* thread at the Physics Forums is the same (they must be, but I can’t quite work it out…).

This doesn’t help me generate values, but I’m looking at that thread, or others for more info. If I figure out the algebra, I’ll let you know.