https://riemannhypothesis.blog/tags/chebyshev/ Recent content in Chebyshev on Understanding the Riemann Hypothesis Hugo -- gohugo.io en markus@recommend.games (Markus Shepherd) markus@recommend.games (Markus Shepherd) Sun, 12 Jan 2014 11:31:23 +0000 https://riemannhypothesis.blog/2014/01/counting-primes-functionally/ Sun, 12 Jan 2014 11:31:23 +0000markus@recommend.games (Markus Shepherd) https://riemannhypothesis.blog/2014/01/counting-primes-functionally/ After all this playing with the \(\zeta\)-function it is time to return to the overall objective of this whole exercise: counting prime numbers. The idea behind analytic number theory is that primes are unpredictable on the small scale, but actually surprising regular on the large scale. This is why we’ll look at certain functions that behave pretty erratically when we look at every single value, but become smooth and “easy” to calculate once we “zoom out” and consider the global properties, the so-called asymptotic.