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Lehmer pair

Pair of zeros of the Riemann zeta function From Wikipedia, the free encyclopedia

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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]

Unsolved problem in mathematics
Are there infinitely many Lehmer pairs?

More precisely, a Lehmer pair can be defined as having the property that their complex coordinates and obey the inequality

for a constant .[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.[4]

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