The zeta zero counting function has been know for at least since the year 1912, maybe even longer back to Riemann, I don't know the history behind it. What I did was to wrap the counting …

Apr 20, 2017 · Wikipedia states that The Riemann zeta function ζ(s) is defined for all complex numbers s ≠ 1. It has zeros at the negative even integers (i.e. at s = −2, −4, −6,...). These are …

Why is the value of the Riemann Zeta function equal to 0 for every even negative number? I assume that even negative refers to the real part of the number, while its imaginary part is 0.

The first derivative for example does not have much zero at the points where the Riemann ζ[s] ζ [s] has. Since the values of the derivatives tell about the multiplicity of the zero, these zeros …

The Euler product is of little to no use in studying the zeros of the Riemann zeta function from what I know. It doesn't converge in the critical strip, for example. Its intrigue is that an object …

Apr 21, 2016 · Also, just because this (and other stuff too) says it is −1/2 − 1 / 2, it still equals +infinity. But we define it differently with analytic continuation. It's more like saying that zeta of …

Sep 14, 2017 · (This doesn't address the specific case of the Riemann zeta function, but is aimed at the OP's more general confusion around infinite products:) An infinite product can be zero …

We now use the fact that the zeta function has a simple pole at s = 1 s = 1 with residue 1 1 (this is, in my opinion, one of the most beautiful elementary things that can be proved about this …

I assume you know the first two ones. The last one can be computed directly from the integral definition of Γ Γ by variable change u = t√ u = t, using ∫+∞ 0 e−u2du = π√ 2 ∫ 0 + ∞ e − u 2 d u …

Edit: I've read this What is so interesting about the zeroes of the Riemann ζ ζ function? but roughly around this point "This formula says that the zeros of the Riemann zeta function …