Explicit formula

Explicit formula

Every non-trivial zero of the Riemann zeta function ζ(s) has real part 1/2. Equivalent forms involve the ξ-function, the explicit formula, and zero-density estimates on the critical strip.

Explicit formula —lemma→ Riemann

Weil–Guinand explicit formula: for a suitable even Schwartz test function h with Fourier transform ĥ, ∑_ρ h((ρ−1/2)/i) = —lemma→ Explicit formula

Explicit formula —implies→ Critical line