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.
[1] They are named after Derrick Henry Lehmer, who discovered the pair of zeros (the 6709th and 6710th zeros of the zeta function).
[2] More precisely, a Lehmer pair can be defined as having the property that their complex coordinates
[3] It is an unsolved problem whether there exist infinitely many Lehmer pairs.
[3] 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.