Zeros of the Riemann zeta function ζ(s) come in two different types. So-called "trivial zeros" occur at all negative even integers s = - 2, -4, -6, ..., and "nontrivial zeros" occur at certain values of t satisfying s congruent σ + i t for s in the "critical strip" 0<σ<1. In general, a nontrivial zero of ζ(s) is denoted ρ, and the nth nontrivial zero with t>0 is commonly denoted ρ_n, with the corresponding value of t being called t_n.

critical line | critical strip | explicit formula | Gram point | Gram's law | Hadamard product | Hilbert-Pólya conjecture | Landau's formula | Lehmer's phenomenon | Li's criterion | Mangoldt function | Montgomery-Odlyzko law | Montgomery's pair correlation conjecture | Riemann hypothesis | Riemann-von Mangoldt formula | Riemann zeta function | xi-function

Bernhard Riemann