Zeta — Riemann Zeta Function and Zero Analysis
Compute the Riemann zeta function ζ(s), find zeros on the critical line, verify the Riemann Hypothesis to a given height, and analyze zero spacing statistics against GUE random matrix predictions. Pur
5 toolszeta
Evaluate
Evaluate ζ(s) at a complex point s = σ + it. Returns real and imaginary parts of the result. Uses Euler-Maclaurin summat
sigmat
Find Zeros
Find zeros of ζ(s) on the critical line (σ=1/2) between t_low and t_high. Returns a list of zero locations with refined
t_lowt_high
Verify Rh
Verify the Riemann Hypothesis up to a given height T on the critical line. Counts expected vs found zeros and checks for
height
Z Function
Evaluate the Riemann-Siegel Z function Z(t), which is real-valued on the critical line. Sign changes of Z(t) indicate ze
t
Gue Comparison
Compare zero spacings against GUE (Gaussian Unitary Ensemble) random matrix theory predictions. Tests the Montgomery-Odl
t_lowt_high