Lehmer pair

In the study of the Riemann hypothesis, a Lehmer pair is a pair of zeros of the Riemann zeta function that are unusually close to each other. They are named after Derrick Henry Lehmer, who discovered the pair of zeros
.
More precisely, a Lehmer pair can be defined as having the property that their complex coordinates and obey the inequality
for a constant.
It is an unsolved problem whether there exist infinitely many Lehmer pairs.
If so, it would imply that the De Bruijn–Newman constant is non-negative,
a fact that has been proven unconditionally by Brad Rodgers and Terence Tao.