Results 171 to 180 of about 48,716 (213)

The Riemann hypothesis and universality of the Riemann zeta-function

Mathematica Slovaca, 2018
We prove that, under the Riemann hypothesis, a wide class of analytic functions can be approximated by shifts ζ(s + iγk), k ∈ ℕ, of the Riemann zeta-function, where γk are imaginary parts of nontrivial zeros of ζ(s).
Ramunas Garunkštis, Antanas Laurincikas   +1 more
exaly   +2 more sources

The Riemann Zeta Function

, 2004
P. Bateman, H. Diamond
semanticscholar   +2 more sources

A Formula on Riemann Zeta Function

The Annals of Mathematics, 1945
2. LEMMA 1. [31 p. 132. Let C be the rectangle whose vertices are iT, -iT, T + iT, T iT running in the positive direction. Let us put F(z) = log cD(-iz), where z = x + iy, the logarithm being defined as follows; we start with a particular determination on x = T and it is real when z = T, and obtain the value at other points by continuous variation ...
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On the Zeros of the Riemann Zeta-Function

Journal of the London Mathematical Society, 1999
\textit{J. E. Littlewood} proved that the Riemann zeta-function \(\zeta(s)\) always has a zero in the strip \(T\leq \text{Im }s\leq T+c/\log\log\log T\) for \(T\) large enough, where \(c\) is an absolute constant [Proc. Lond. Math. Soc. 22, 234-242 (1924; JFM 50.0229.04)]; \textit{E. C. Titchmarsh} gave a simpler proof [Proc. Camb. Philos. Soc. 28, 273-
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A Multicomplex Riemann Zeta Function

Advances in Applied Clifford Algebras, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Reid, Frederick Lyall, van Gorder, Robert A.   +1 more
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Blockchain and the Riemann Zeta Function

2021
Proof of Work (PoW) mechanisms used as part of the consensus mechanisms in block chains often have a major drawback namely that resources are only spent on doing the PoW and nothing else. In this paper we propose an adaption of hash based PoW’s. This adaption consists in two aspects, firstly by embedding the space of the hash’s, \(\mathcal{H}\), in the
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The Riemann zeta function

2020
As Euler noted, the fact that the series (11.0.1) diverges at \(s=1\) gives another proof that the set of primes is infinite—in fact \(\sum _p(1/p)\) diverges. (This is only the simplest of the connections between properties of the zeta function and properties of primes.)
Richard Beals, Roderick S. C. Wong
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On the zeros of the Riemann zeta function

Commentarii mathematici Universitatis Sancti Pauli = Rikkyo Daigaku sugaku zasshi, 2002
This paper brings forth estimates of iterated integrals for the classical function \(S(T)\) of analytic number theory, namely \[ S(T) = \tfrac 1\pi\arg\zeta(\tfrac 12+ iT) \] when \(T\) is not equal to any \(\gamma\), where \(\rho = \beta + i\gamma\) denotes generic complex zeros of the Riemann zeta-function \(\zeta(s)\).
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Riemann zeta matrix function

2015
In this study, obtaining the matrix analog of the Euler's reflection formula for the classical gamma function we expand the domain of the gamma matrix function and give a infinite product expansion of sin pi xP. Furthermore we define Riemann zeta matrix function and evaluate some other matrix integrals.
KARGIN, Levent, KURT, Veli
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The Riemann Zeta-Function

Nature, 1952
The Theory of the Riemann Zeta-Function By Prof. E. C. Titchmarsh. Pp. vii + 346. (Oxford: Clarendon Press; London: Oxford University Press, 1951.) 40s. net.
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