Effective version of self-approximation for the Riemann zeta function
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DOI: 10.1002/mana.201400107
Abstract: In the paper we prove an effective version of self-approximation for the Riemann zeta function. read more here.
Keywords: approximation riemann; zeta function; effective version; version self ... See more keywords
On discrete universality of the Riemann zeta-function with respect to uniformly distributed shifts
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DOI: 10.1007/s00013-016-0998-8
Abstract: The Voronin universality theorem asserts that a wide class of analytic functions can be approximated by shifts $$\zeta (s+i\tau )$$ζ(s+iτ), $$\tau \in \mathbb {R}$$τ∈R, of the Riemann zeta-function. In the paper, we obtain a universality… read more here.
Keywords: zeta function; uniformly distributed; universality; riemann zeta ... See more keywords
Computing Extremely Large Values of the Riemann Zeta Function
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DOI: 10.1007/s10723-017-9416-0
Abstract: The paper summarizes the computation results pursuing peak values of the Riemann zeta function. The computing method is based on the RS-Peak algorithm by which we are able to solve simultaneous Diophantine approximation problems efficiently.… read more here.
Keywords: zeta function; function computing; computing extremely; riemann zeta ... See more keywords
Zeros of Riemann’s Zeta Functions in the Line z=1/2+it0
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DOI: 10.1007/s10948-019-05243-0
Abstract: It was found that, in addition to trivial zeros in points (z = − 2N, N = 1, 2…, natural numbers), the Riemann’s zeta function ζ(z) has zeros only on the line {$$ z=\frac{1}{2}+\mathrm{i}{\mathrm{t}}_0 $$, t0 is real}. All zeros are… read more here.
Keywords: zeta functions; line; zeros riemann; riemann zeta ... See more keywords
Transformation of generalized multiple Riemann zeta type sums with repeated arguments
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DOI: 10.1016/j.jmaa.2016.12.023
Abstract: Abstract The aim of this paper is the study of a transformation dealing with the general K-fold infinite series of the form ∑ n 1 ≥ ⋯ ≥ n K ≥ 1 ∏ j =… read more here.
Keywords: repeated arguments; transformation; riemann zeta; zeta ... See more keywords
Pair correlation of zeros of the real and imaginary parts of the Riemann zeta-function
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DOI: 10.1016/j.jnt.2017.10.024
Abstract: Abstract We show that if the Riemann Hypothesis is true for the Riemann zeta-function, ζ ( s ) , and 0 a 1 / 2 , then all but a finite number of the zeros… read more here.
Keywords: zeta function; pair correlation; correlation zeros; riemann zeta ... See more keywords
High pseudomoments of the Riemann zeta function
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DOI: 10.1016/j.jnt.2018.10.001
Abstract: Abstract The pseudomoments of the Riemann zeta function, denoted M k ( N ) , are defined as the 2kth integral moments of the Nth partial sum of ζ ( s ) on the critical… read more here.
Keywords: zeta function; pseudomoments riemann; high pseudomoments; riemann zeta ... See more keywords
Universality of the Riemann zeta-function in short intervals
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DOI: 10.1016/j.jnt.2019.04.006
Abstract: Abstract By the Voronin theorem, the set of shifts of the Riemann zeta-function ζ ( s + i τ ) , s = σ + i t , τ ∈ R , that approximate any… read more here.
Keywords: function short; zeta function; universality riemann; riemann zeta ... See more keywords
Formulas for the Riemann zeta-function and certain Dirichlet series
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DOI: 10.1080/10652469.2018.1514394
Abstract: ABSTRACT Using known theta identities and formulas of S. Ramanujan and G. Hardy among others we prove several formulas for the Riemann zeta-function and two Dirichlet series. read more here.
Keywords: zeta function; dirichlet series; formulas riemann; riemann zeta ... See more keywords
A generalization of functional limit theorems on the Riemann zeta process
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DOI: 10.18910/73631
Abstract: $\zeta(\cdot)$ being the Riemann zeta function, $\zeta_{\sigma}(t) := \frac{\zeta(\sigma + i t)}{\zeta(\sigma)}$ is, for $\sigma > 1$, a characteristic function of some infinitely divisible distribution $\mu_{\sigma}$. A process with time parameter $\sigma$ having $\mu_{\sigma}$ as… read more here.
Keywords: functional limit; sigma; process; riemann zeta ... See more keywords
Joint Discrete Approximation of Analytic Functions by Shifts of the Riemann Zeta-Function Twisted by Gram Points
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DOI: 10.3390/math11030565
Abstract: Let θ(t) denote the increment of the argument of the product π−s/2Γ(s/2) along the segment connecting the points s=1/2 and s=1/2+it, and tn denote the solution of the equation θ(t)=(n−1)π, n=0,1,⋯. The numbers tn are… read more here.
Keywords: functions shifts; gram points; riemann zeta; analytic functions ... See more keywords