Results 41 to 50 of about 640,811 (318)
Some Observations on the Greatest Prime Factor of an Integer
Annales Mathematicae Silesianae, 2023 We examine the multiplicity of the greatest prime factor in k-full numbers and k-free numbers. We generalize a well-known result on greatest prime factors and obtain formulas related with the Riemann zeta function.
Jakimczuk Rafael
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Orbit Growth of Shift Spaces Induced by Bouquet Graphs and Dyck Shifts
Mathematics, 2021 For a discrete dynamical system, the prime orbit and Mertens’ orbit counting functions describe the growth of its closed orbits in a certain way. The asymptotic behaviours of these counting functions can be determined via Artin–Mazur zeta function of the
Azmeer Nordin, Mohd Salmi Md Noorani
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The Derivation of the Riemann Analytic Continuation Formula from the Euler’s Quadratic Equation
Journal of Nigerian Society of Physical Sciences, 2022 The analysis of the derivation of the Riemann Analytic Continuation Formula from Euler’s Quadratic Equation is presented in this paper. The connections between the roots of Euler’s quadratic equation and the Analytic Continuation Formula of the Riemann ...
Opeyemi O. Enoch +2 more
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Gaps between primes, and the pair correlation of zeros of the zeta-function [PDF]
Acta Arithmetica, 1982 D. R. Heath‐Brown
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On the logarithm of the Riemann zeta-function near the nontrivial zeros [PDF]
Transactions of the American Mathematical Society, 2020 Assuming the Riemann hypothesis and Montgomery's Pair Correlation Conjecture, we investigate the distribution of the sequences $(\log|\zeta(\rho+z)|)$ and $(\arg\zeta(\rho+z)).$ Here $\rho=\frac12+i\gamma$ runs over the nontrivial zeros of the zeta ...
F. Çiçek
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Weyl asymptotics for perturbations of Morse potential and connections to the Riemann zeta function
Concrete Operators, 2023 Let N(T;V)N\left(T;\hspace{0.33em}V) denote the number of eigenvalues of the Schrödinger operator −y″+Vy-{y}^{^{\prime\prime} }+Vy with absolute value less than TT. This article studies the Weyl asymptotics of perturbations of the Schrödinger operator −y″
Rahm Rob
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Boletim da Sociedade Paranaense de Matemática, 2022 Let $K=Q(\sqrt{d})$ be a quadratic field with discriminant $d$. It is shown that $\sum\limits_{(\frac{d}{p})=+1,_{p~ prime}}\frac{1}{p}$ and $\sum\limits_{(\frac{d}{q})=-1,_{q~ prime}}\frac{1}{q}$ are both divergent.
G. Sudhaamsh Mohan Reddy +2 more
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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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On the value-distribution of iterated integrals of the logarithm of the Riemann zeta-function I: Denseness [PDF]
, 2020 We consider iterated integrals of logζ(s){\log\zeta(s)} on certain vertical and horizontal lines. Here, the function ζ(s){\zeta(s)} is the Riemann zeta-function. It is a well-known open problem whether or not the values of the Riemann zeta-function on
K. Endo, S. Inoue
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A singular series average and the zeros of the Riemann zeta-function [PDF]
Acta Arithmetica, 2020 We show that the Riesz mean of the singular series in the Goldbach and the Hardy-Littlewood prime-pair conjectures has an asymptotic formula with an error term that can be expressed as an explicit formula that depends on the zeros of the Riemann zeta ...
D. Goldston, Ade Irma Suriajaya
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