Riemann ζ Zeros on the Critical Line — Gram Points

Hardy Z-function:
Z(t) = e^{iθ(t)}ζ(½+it)
Z(t) is real-valued

Riemann-Siegel θ:
θ(t) ≈ t/2·ln(t/2π) − t/2 − π/8
+ 1/(48t) + ...

Zeros of ζ(½+it):
↔ sign changes of Z(t)

Gram points gₙ: θ(gₙ)=nπ
"Gram's law": Z(gₙ) > 0
(fails for ~27% of pairs)

First zeros t₁ ≈ 14.135
t₂ ≈ 21.022, t₃ ≈ 25.011
~10^21 zeros verified on line