https://riemannhypothesis.blog/tags/newton/ Recent content in Newton on Understanding the Riemann Hypothesis Hugo -- gohugo.io en markus@recommend.games (Markus Shepherd) markus@recommend.games (Markus Shepherd) Sun, 06 Apr 2014 14:13:42 +0000 https://riemannhypothesis.blog/2014/04/from-zeta-to-j-and-back-and-yet-again-back/ Sun, 06 Apr 2014 14:13:42 +0000markus@recommend.games (Markus Shepherd) https://riemannhypothesis.blog/2014/04/from-zeta-to-j-and-back-and-yet-again-back/ We know a lot about the \(\zeta\) and \(\xi\)-functions, we’ve learnt all about the different prime counting functions, most notably \(J(x)\), so it’s high time we found a connection between the two. Probably not too surprisingly, the crucial link is our good friend, the Euler product \[ \zeta(s)=\prod_{p}(1-p^{-s})^{-1}. \] What we want to develop now is a version of this product that will suit us to find a formula that magically can count primes.