structural:summarization, structural:reformatting, information:extraction
Other results

It is known that there are infinitely many zeros on the critical line. Littlewood showed that if the sequence (γ) contains the imaginary parts of all zeros in the upper half-plane in ascending order, then

The critical line theorem asserts that a positive proportion of the nontrivial zeros lies on the critical line. (The Riemann hypothesis would imply that this proportion is 1.)

In the critical strip, the zero with smallest non-negative imaginary part is 1 / 2 + 14.13472514... i (OEIS: A058303). The fact that

for all complex s ≠ 1 implies that the zeros of the Riemann zeta function are symmetric about the real axis. Combining this symmetry with the functional equation, furthermore, one sees that the non-trivial zeros are symmetric about the critical line Re(s) = 1 / 2.

It is also known that no zeros lie on the line with real part 1.