An approximation to zeros of the Riemann zeta function using fractional calculus [PDF]
A novel iterative method to approximate the zeros of the Riemann zeta function is presented. This iterative method, valid for one and several variables, uses the properties of fractional calculus, in particular the fact that the fractional derivatives of
A. Torres-Hernandez, F. Brambila-Paz
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Complete basis set extrapolation of electronic correlation energies using the Riemann zeta function. [PDF]
In this communication we demonstrate the effectiveness of the method of complete basis set (CBS) extrapolation of correlation energies based on the application of the Riemann zeta function.
M. Lesiuk, B. Jeziorski
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Precalculated arrays-based algorithms for the calculation of the Riemann zeta-function
In this paper, we continue the study of efficient algorithms for the computation of the Riemann zeta function on the complex plane. We introduce two precalculated arrays-based modifications of MB-method.
Lukas Kuzma +2 more
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New Results Involving Riemann Zeta Function Using Its Distributional Representation
The relation of special functions with fractional integral transforms has a great influence on modern science and research. For example, an old special function, namely, the Mittag–Leffler function, became the queen of fractional calculus because its ...
Asifa Tassaddiq, Rekha Srivastava
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Decoupling, exponential sums and the Riemann zeta function [PDF]
We establish a new decoupling inequality for curves in the spirit of [B-D1], [B-D2] which implies a new mean value theorem for certain exponential sums crucial to the Bombieri-Iwaniec method as developed further in [H].
J. Bourgain
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Partial sums of random multiplicative functions and extreme values of a model for the Riemann zeta function [PDF]
We consider partial sums of a weighted Steinhaus random multiplicative function and view this as a model for the Riemann zeta function. We give a description of the tails and high moments of this object.
Marco Aymone, W. Heap, J. Zhao
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Maximum of the Riemann Zeta Function on a Short Interval of the Critical Line [PDF]
We prove the leading order of a conjecture by Fyodorov, Hiary, and Keating about the maximum of the Riemann zeta function on random intervals along the critical line.
L. Arguin +4 more
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On the Riemann zeta-function I [PDF]
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
openaire +2 more sources
Fungsi Zeta Riemann Genap Menggunakan Bilangan Bernoulli
In this article, we study about the value of Riemann Zeta Function for even numbers using Bernoulli number. First, we give some basic theory about Bernoulli number and Riemann Zeta function.
Ikhsan Maulidi +2 more
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Some Numerical Significance of the Riemann Zeta Function
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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