Results 61 to 70 of about 1,611,376 (286)
On a Fractal Representation of the Density of Primes
Recoletos Multidisciplinary Research Journal, 2014 The number of primes less or equal to a real number x, π(x), has been approximated in the past by the reciprocal of the logarithm of the number x. Such an approximation works well when x is large but it can be poor when x is small.
Joy Mirasol, Efren O. Barabat
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Numerical Calculations to Grasp a Mathematical Issue Such as the Riemann Hypothesis
Information, 2020 This article presents the use of data processing to apprehend mathematical questions such as the Riemann Hypothesis (RH) by numerical calculation. Calculations are performed alongside graphs of the argument of the complex numbers ζ ( x + i y ...
Michel Riguidel
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New Analytical Formulas for the Rank of Farey Fractions and Estimates of the Local Discrepancy
MathematicsNew analytical formulas are derived for the rank and the local discrepancy of Farey fractions. The new rank formula is applicable to all Farey fractions and involves sums of a lower order compared to the searched one.
Rogelio Tomás García
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Bounding Sn (t) on the Riemann hypothesis [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2017 Let $S(t) = {1}/{\pi} \arg \zeta \big(\hh + it \big)$ be the argument of the Riemann zeta-function at the point 1/2 + it. For n ⩾ 1 and t > 0 define its iterates $$\begin{equation*} S_n(t) = \int_0^t S_{n-1}(\tau) \,\d\tau\, + \delta_n\,, \end{equation*}
E. Carneiro, Andrés Chirre
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On Balazard, Saias, and Yor's equivalence to the Riemann Hypothesis
, 2013 Balazard, Saias, and Yor proved that the Riemann Hypothesis is equivalent to a certain weighted integral of the logarithm of the Riemann zeta-function along the critical line equaling zero.
Bui, H. M. +2 more
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Interval‐valued Caputo–Fabrizio fractional derivative in continuous programming
Asian Journal of Control, EarlyView.Abstract This study investigates a novel class of variational programming problems characterized by fractional interval values, formulated under the Caputo–Fabrizio fractional derivative with an exponential kernel. Invex and generalized invex functions are used to discuss the Mond–Weir‐type dual problem for the considered variational problem.
Krishna Kummari +2 more
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Development of a New Zeta Formula and Its Role in Riemann Hypothesis and Quantum Physics
Mathematics, 2023 In this study, we investigated a new zeta formula in which the zeta function can be expressed as the sum of an infinite series of delta and cosine functions.
Saadeldin Abdelaziz +2 more
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The Lindelöf hypothesis for primes is equivalent to the Riemann hypothesis
, 2020 We recast the classical Lindelöf hypothesis as an estimate for the sums ∑ n ≤ x n − i t \sum _ ...
S. Gonek, S. W. Graham, Yoonbok Lee
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A probabilistic diagnostic for Laplace approximations: Introduction and experimentation
Canadian Journal of Statistics, EarlyView.Abstract Many models require integrals of high‐dimensional functions: for instance, to obtain marginal likelihoods. Such integrals may be intractable, or too expensive to compute numerically. Instead, we can use the Laplace approximation (LA). The LA is exact if the function is proportional to a normal density; its effectiveness therefore depends on ...
Shaun McDonald, Dave Campbell
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Convergence properties of dynamic mode decomposition for analytic interval maps
Communications on Pure and Applied Mathematics, EarlyView.Abstract Extended dynamic mode decomposition (EDMD) is a data‐driven algorithm for approximating spectral data of the Koopman operator associated to a dynamical system, combining a Galerkin method with N$N$ functions and a quadrature method with M$M$ quadrature nodes.
Elliz Akindji +3 more
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