 Three-four-one zero-free-region argument

ID: three-four-one-zero-free-region-argument

For

F = - ζ^{'} / ζ

and

σ > 1

, positivity of

3 + 4 cos θ + cos 2 θ = 2 (1 + cos θ)^{2}

term by term in the Euler product gives

3 F (σ) + 4ℜ F (σ + i t) + ℜ F (σ + 2 i t) \geq 0.

Comparing this with the pole of

F

at one and the local poles of

ζ^{'} / ζ

at zeros proves the classical zero-free region.

 New to topics? Read the docs here!