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Lehmer pair

Index 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. [1]

9 relations: Acta Mathematica, Constructive Approximation, De Bruijn–Newman constant, Derrick Henry Lehmer, Montgomery's pair correlation conjecture, Riemann hypothesis, Riemann zeta function, Terence Tao, Zero of a function.

Acta Mathematica

Acta Mathematica is a peer-reviewed open-access scientific journal covering research in all fields of mathematics.

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Constructive Approximation

Constructive Approximation is "an international mathematics journal dedicated to Approximations and Expansions and related research in computation, function theory, functional analysis, interpolation spaces and interpolation of operators, numerical analysis, space of functions, special functions, and applications.".

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De Bruijn–Newman constant

The De Bruijn–Newman constant, denoted by Λ and named after Nicolaas Govert de Bruijn and Charles M. Newman, is a mathematical constant defined via the zeros of a certain function H(λ, z), where λ is a real parameter and z is a complex variable.

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Derrick Henry Lehmer

Derrick Henry "Dick" Lehmer (February 23, 1905 – May 22, 1991) was an American mathematician who refined Édouard Lucas' work in the 1930s and devised the Lucas–Lehmer test for Mersenne primes.

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Montgomery's pair correlation conjecture

In mathematics, Montgomery's pair correlation conjecture is a conjecture made by that the pair correlation between pairs of zeros of the Riemann zeta function (normalized to have unit average spacing) is which, as Freeman Dyson pointed out to him, is the same as the pair correlation function of random Hermitian matrices.

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Riemann hypothesis

In mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part.

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Riemann zeta function

The Riemann zeta function or Euler–Riemann zeta function,, is a function of a complex variable s that analytically continues the sum of the Dirichlet series which converges when the real part of is greater than 1.

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Terence Tao

Terence Chi-Shen Tao (born 17 July 1975) is an Australian-American mathematician who has worked in various areas of mathematics.

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Zero of a function

In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x).

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References

[1] https://en.wikipedia.org/wiki/Lehmer_pair

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