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In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1/2. Many consider it to be the most important unsolved problem in pure mathematics. It is of great interest in number theory because it implies results about the distribution of prime numbers. It was proposed by Bernhard Riemann (1859), after whom it is named.
In mathematics, Montgomery's pair correlation conjecture is a conjecture made by Hugh Montgomery (1973) that the pair correlation between pairs of zeros of the Riemann zeta function is
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
References
- ↑ Zeta Finished – Free-DC Forum
- ↑ Ed Pegg Jr. «Ten Trillion Zeta Zeros»
- ↑ "ZetaGrid - News". 2010-11-18. Archived from the original on 2010-11-18. Retrieved 2023-06-04.
- ↑ Yannick Saouter, Xavier Gourdon and Patrick Demichel. An improved lower bound for the de Bruijn-Newman constant. Math. Comp. 80 (2011) 2283. MR 2813360.
- ↑ Yannick Saouter and Patrick Demichel. A sharp region where π(x)−li(x) is positive. Math. Comp. 79 (2010) 2398. MR 2684372.
