منابع مشابه
Simple Zeros of the Riemann Zeta-function
Assuming the Riemann Hypothesis, Montgomery and Taylor showed that at least 67.25% of the zeros of the Riemann zeta-function are simple. Using Montgomery and Taylor's argument together with an elementary combinatorial argument, we prove that assuming the Riemann Hypothesis at least 67.275% of the zeros are simple.
متن کاملDistribution of the zeros of the Riemann Zeta function
One of the most celebrated problem of mathematics is the Riemann hypothesis which states that all the non trivial zeros of the Zeta-function lie on the critical line <(s) = 1/2. Even if this famous problem is unsolved for so long, a lot of things are known about the zeros of ζ(s) and we expose here the most classical related results : all the non trivial zeros lie in the critical strip, the num...
متن کاملLarge Gaps between the Zeros of the Riemann Zeta Function
If the Riemann hypothesis (RH) is true then the non-trivial zeros of the Riemann zeta function, ζ(s), satisfy 1/2+iγn with γn ∈ R. Riemann noted that the argument principle implies that number of zeros of ζ(s) in the box with vertices 0, 1, 1 + iT, and iT is N(T ) ∼ (T/2π) log (T/2πe). This implies that on average (γn+1 − γn) ≈ 2π/ log γn and hence the average spacing of the sequence γ̂n = γn lo...
متن کاملHamiltonian for the Zeros of the Riemann Zeta Function.
A Hamiltonian operator H[over ^] is constructed with the property that if the eigenfunctions obey a suitable boundary condition, then the associated eigenvalues correspond to the nontrivial zeros of the Riemann zeta function. The classical limit of H[over ^] is 2xp, which is consistent with the Berry-Keating conjecture. While H[over ^] is not Hermitian in the conventional sense, iH[over ^] is P...
متن کاملZeros of the Riemann Zeta-Function on the Critical Line
It was shown by Selberg [3] that the Riemann Zeta-function has at least cT log T zeros on the critical line up to height T, for some positive absolute constant c. Indeed Selberg’s method counts only zeros of odd order, and counts each such zero once only, regardless of its multiplicity. With this in mind we shall write γ̂i for the distinct ordinates of zeros of ζ(s) on the critical line of odd m...
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ژورنال
عنوان ژورنال: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
سال: 1935
ISSN: 1364-5021,1471-2946
DOI: 10.1098/rspa.1935.0146