Results 11 to 20 of about 637 (178)
On the Functional Independence of the Riemann Zeta-Function
Mathematical Modelling and Analysis, 2023 In 1973, Voronin proved the functional independence of the Riemann zeta-function ζ(s), i.e., that ζ(s) and its derivatives do not satisfy a certain equation with continuous functions. In the paper, we obtain a joint version of the Voronin theorem.
Virginija Garbaliauskienė +2 more
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On Maslanka's Representation for the Riemann Zeta Function [PDF]
International Journal of Mathematics and Mathematical Sciences, 2010 A rigorous proof is given of the hypergeometric-like representation of the Riemann zeta function 𝜁(𝑠) discovered by Maslanka as a series of Pochhamer polynomials with coefficients depending on the values of 𝜁 at the positive even integers.
Luis Báez-Duarte
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Riemann’s zeta function and beyond [PDF]
Bulletin of the American Mathematical Society, 2003 In recent years L L -functions and their analytic properties have assumed a central role in number theory and automorphic ...
Gelbart, Stephen S., Miller, Stephen D.
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A stochastic interpretation of the Riemann zeta function. [PDF]
Proc Natl Acad Sci U S A, 1993 We give a stochastic process for which the terms of the Riemann zeta function occur as the probability distributions of the elementary random variables of the process.
Alexander KS, Baclawski K, Rota GC.
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Amplitudes and the Riemann Zeta Function [PDF]
Physical Review Letters, 2021 Physical properties of scattering amplitudes are mapped to the Riemann zeta function. Specifically, a closed-form amplitude is constructed, describing the tree-level exchange of a tower with masses $m_n^2 = μ_n^2$, where $ζ\left(\frac{1}{2} \pm iμ_n\right) = 0$.
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On the Riemann zeta-function I [PDF]
Bulletin of the Australian Mathematical Society, 1976 We prove an approximation formula for the Riemann zeta function. We show that a classical theorem:uniformly in the domain ½ ≤ σ < 1, is an immediate consequence of our approximation formula. Our method is real and free from complex analysis.
Izumi, Masako, Izumi, Shin-ichi
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Some Numerical Significance of the Riemann Zeta Function
Recent Advances in Natural Sciences, 2023 In this paper, the Riemann analytic continuation formula (RACF) is derived from Euler’s quadratic equation. A nonlinear function and a polynomial function that were required in the derivation were also obtained.
Opeyemi O. Enoch, Lukman O. Salaudeen
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General infinite series evaluations involving Fibonacci numbers and the Riemann zeta function
Математичні Студії, 2021 The purpose of this paper is to present closed forms for various types of infinite series involving Fibonacci (Lucas) numbers and the Riemann zeta function at integer arguments.
R. Frontczak, T. Goy
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Questions around the nontrivial zeros of the Riemann zeta-function. Computations and classifications
Mathematical Modelling and Analysis, 2011 We study the sequence of nontrivial zeros of the Riemann zeta-function with respect to sequences of zeros of other related functions, namely, the Hurwitz zeta-function and the derivative of Riemann's zeta-function.
Ramūnas Garunkštis, Joern Steuding
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Sonification of the Riemann Zeta Function [PDF]
Proceedings of the 25th International Conference on Auditory Display (ICAD 2019), 2019 The Riemann zeta function is one of the great wonders of mathematics, with a deep and still not fully solved connection to the prime numbers. It is defined via an infinite sum analogous to Fourier additive synthesis, and can be calculated in various ways.
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