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A Multicomplex Riemann Zeta Function

Advances in Applied Clifford Algebras, 2012
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Reid, Frederick Lyall, van Gorder, Robert A.   +1 more
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Riemann Zeta Function

2021
Topic of this chapter is the Riemann zeta function and its non-trivial zeros. The evaluation of the Riemann zeta function is based on a series expansion and if necessary additionally on transforming the function argument. The first 50 non-trivial zeros are table based, additional non-trivial zeros will be numerically evaluated.
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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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Riemann Zeta Function

2011
Riemann zeta function represents an important tool in analytical number theory with various applications in quantum mechanics, probability theory and statistics. First introduced by Bernhard Riemann in 1859, zeta function is a central object of many outstanding problems.
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Riemann’s Zeta Function

2018
The zeta function is defined for ℜ(s) > 1 by $$\displaystyle \zeta (s) = \sum _{n=1}^{+\infty } \frac {1}{n^s}. $$
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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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On the extreme values of the Riemann zeta function on random intervals of the critical line

, 2016
In the present paper, we show that under the Riemann hypothesis, and for fixed $$h, \epsilon > 0$$h,ϵ>0, the supremum of the real and the imaginary parts of $$\log \zeta (1/2 + it)$$logζ(1/2+it) for $$t \in [UT -h, UT + h]$$t∈[UT-h,UT+h] are in the ...
J. Najnudel
semanticscholar   +1 more source

Riemann Zeta Function

We prove that the unique shift ε = φ − 1 — where φ = (1 + √5)/2 is the Golden Ratio — makes the 2-regularized Fredholm determinant of the diagonal operator Aₛ+ε on ℓ²(primes) equal (up to an entire, nowhere-vanishing factor) to ζ(s)⁻¹. Explicitly,     det₂(I − Aₛ+φ−1 · E_φ(s)) = ζ(s)⁻¹, for Re s > ½,   where E_φ is an elementary exponential built ...
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Riemann $$\zeta $$ζ-Function

2019
This section is about the properties of the Riemann \(\zeta \)-function. Here we also discuss Riemann hypothesis and the uses of the \(\zeta \)-function in the calculations of functional integrals.
Valeriya Akhmedova, Emil T. Akhmedov
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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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